Daily Papers

The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat -- the equilateral member of the continuum to which it belongs -- is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only chiral non-periodic tilings based on a hierarchical substitution system.

In chemistry and biochemistry, chirality represents the structural asymmetry characterized by non-superimposable mirror images for a material like DNA. In physics, however, chirality commonly refers to the spin-momentum locking of a particle or quasiparticle in the momentum space. While seemingly disconnected, structural chirality in molecules and crystals can drive electronic chirality through orbital-momentum locking, i.e. chirality can be transferred from the atomic geometry to electronic orbitals. Electronic chirality provides an insightful understanding of the chirality-induced spin selectivity (CISS), in which electrons exhibit salient spin polarization after going through a chiral material, and electric magnetochiral anisotropy (EMCA), which is characterized by the diode-like transport. It further gives rise to new phenomena, such as anomalous circularly polarized light emission (ACPLE), in which the light handedness relies on the emission direction. These chirality-driven effects will generate broad impacts in fundamental science and technology applications in spintronics, optoelectronics, and biochemistry.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete Z_2 symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous U(1) symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: R_1sim t^{-1} at early times and R_1sim t^{-1/z} at long times, with z set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with z=2 and z=4, which are excellent agreement with the theoretical predictions.

Single-minus tree-level n-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into n-1 plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

We study the mixing between a generic axion-like particle (ALP) and the light pseudoscalar mesons within chiral perturbation theory (χPT), and its consequences for low-energy scattering and decay processes. Starting from the most general ALP effective Lagrangian, we derive the ALP-meson kinetic and mass mixing induced at leading order in the ALP decay constant and isospin breaking for arbitrary ALP masses. As a result, we obtain the physical ALP mass to O(F^2/f_a^2), recovering the QCD-axion limit and finding that any ALP with a vanishing bare mass shares the QCD-axion mass. We provide a compact parameterization of every four-body amplitude involving pseudoscalar mesons and an arbitrary number of ALPs. As an illustration, we show the KKto P^0a scattering. The framework applies for general ALP masses and couplings and consistently incorporates isospin breaking, essential for otherwise forbidden processes.

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension Delta (Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in different dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4+epsilon dimensions. As an example of the second type we consider the U(N)times U(M) model in 4-epsilon dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.

We study two-point functions of chiral primary operators in N=4 Super Yang-Mills in the presence of a half-BPS surface defect. Such a defect preserves only the diagonal combination of transverse rotations and of a global U(1) R-symmetry, so that the correlator depends on one additional cross-ratio and splits into sectors of definite angular charge. We solve the superconformal Ward identities and construct the bulk and defect superconformal blocks in all sectors, including the charged ones, which have no analogue for defects preserving transverse rotations. The solution contains a holomorphic sector, which we fix non-perturbatively by mapping it to a chiral algebra correlator. We extend this map to defects breaking transverse rotations, where it requires a redefinition of the modes of the two-dimensional current algebra, and use it to fix the charged sectors as well. We then use the defect dispersion relation to reconstruct the full correlator of the dimension-two chiral primary at leading order at large N and strong coupling. In the charged sectors long multiplets are absent and the answer is conjecturally exact in both N and the coupling; expanding it at weak coupling, we find perfect agreement with known results. From these correlators we extract infinitely many new pieces of defect CFT data. Finally, we reproduce the strong-coupling answer by an independent Witten diagram bootstrap on the rotation-invariant locus.

We present the quark weak-mixing component of a Froggatt--Nielsen program, with one flavon and three messengers, in which a single hierarchy parameter B (with εequiv 1/B) and a rational-exponent ``B-lattice'' organize fermion Yukawa textures. Building on companion mass-fit work, we translate the lattice into sharp predictions for quark mixing. The four-magnitude parameterization serves as a practical interface between the flavon Yukawa textures and quark weak mixing observables, yielding coefficient-free ratio tests of the lattice structure.

Riemannian four-manifolds in which the triple contraction of the curvature tensor against itself yields a functional multiple of the metric are called weakly Einstein. We focus on weakly Einstein K\"ahler surfaces. We provide several conditions characterizing those K\"ahler surfaces which are weakly Einstein, classify weakly Einstein K\"ahler surfaces having some specific additional properties, and construct new examples.

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho{rmr}ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

At high energies, the dynamics of a plasma with charged fermions can be described in terms of chiral magnetohydrodynamics. Using direct numerical simulations, we demonstrate that chiral magnetic waves (CMWs) can produce a chiral asymmetry μ_5 = μ_L - μ_R from a spatially fluctuating (inhomogeneous) chemical potential μ= μ_L + μ_R, where μ_L and μ_R are the chemical potentials of left- and right-handed electrically charged fermions, respectively. If the frequency of the CMW is less than or comparable to the characteristic growth rate of the chiral dynamo instability, the magnetic field can be amplified on small spatial scales. The growth rate of this small-scale chiral dynamo instability is determined by the spatial maximum value of μ_5 fluctuations. Therefore, the magnetic field amplification occurs during periods when μ_5 reaches temporal maxima during the CMW. If the small-scale chiral dynamo instability leads to a magnetic field strength that exceeds a critical value, which depends on the resistivity and the initial value of μ, magnetically dominated turbulence is produced. Turbulence gives rise to a large-scale dynamo instability, which we find to be caused by the magnetic alpha effect. Our results have consequences for the dynamics of certain high-energy plasmas, such as the early Universe.

Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-χ, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar χ sets the direction of a relative rotation on latent query--key blocks, giving a Chiral-RoPE that reflection inverts rather than leaves fixed. A C_2 projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-χ leads every central-ECD output and improves axial Rotation and Symbol by 12.6% and 7.9% over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the C_2 projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.

The twist-grain-boundary (TGB) phases, characterized by a periodic, helical arrangement of blocks made of polar smectic phases, SmAF and SmCF, have been discovered. They have been observed for rod-like molecules with a strong longitudinal dipole moment, featuring an (S)-2-methylbutyl end group having only weak twisting power, and emerge below the antiferroelectric SmAAF phase, where the lamellar structure is already well established. It is suggested that the structure is governed by electrostatic interactions amplified by weak chiral forces, in striking contrast to the mechanism of TGB phase formation found in non-polar materials. The TGB phases exhibit light selective reflection in the visible range, while the value of electric polarization confirms an almost perfectly ordered dipole alignment.

The back-to-back limit of the energy-energy correlator (EEC) exhibits a finite plateau, capturing the evolution from perturbative soft-collinear radiation at weak coupling to string dynamics at strong coupling. At weak coupling, we resum its leading and next-to-leading-power logarithms through N^3LL in mathcal N=4 SYM, including non-planar contributions. Combining this weak-coupling endpoint with bootstrap and strong-coupling data, we construct an interpolation for the plateau height from weak to strong coupling. The calculation uses a human-in-the-loop agentic workflow.

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

The emergence of spin-polarized electrons from nonmagnetic chiral molecules and crystals is called Chirality-induced spin selectivity (CISS). A chiral phonon of definite wavevector q can strongly enhance it, but near equilibrium the two helicities +q and -q are equally populated: they are time-reversal partners and their contributions cancel. We show that in a biased chiral conductor the current causes the phonon of one helicity to damp less than the other. The damping asymmetry is odd in the current, odd under qrightarrow-q, invariant under a mirror that reverses the structural handedness, and equal, mode for mode, to the current-induced nonconservative Berry force on the phonon coordinate. Closing the phonon kinetics with a rate equation turns the asymmetry into a net lattice helicity: at any finite bias one helicity is preferentially populated, with no threshold, growing linearly with the current as Vrightarrow0; above a threshold that helicity becomes a self-sustained coherent travelling wave. We demonstrate this effect in elemental tellurium, treated as an open quantum system (electronic Hamiltonian, phonon bath, and electron-phonon coupling) within a quasi-ab initio framework. The electronic Hamiltonian is supplied by a vertex-corrected quasiparticle self-consistent GW (QSGW) potential with spin-orbit coupling; nuclear displacements are modeled with a machine-learned interatomic potential, which yields chiral phonon modes at finite pm q_z on the Γ-A line. The perturbation to the electronic Hamiltonian from a nuclear displacement is approximated by a frozen-phonon deformation potential. No optical pump is needed: a bias alone drives the current and selects the phonon helicity; reversing the current reverses the selection.

We consider the D4-D8-D8 brane system which serves as ultraviolet completion of the Nambu-Jona-Lasinio model, where the only degrees of freedom carrying baryon charge are fermions. By turning on chemical potential for this charge one may expect the formation of the Fermi liquid ground state. At strong coupling we use the dual holographic description to investigate the responses of the system to small perturbations. In the chirally symmetric phase we find that the density dependent part of the heat capacity vanishes linearly with temperature. We also observe a zero sound excitation in the collisionless regime, whose speed is equal to that of normal sound in the hydrodynamic regime. Both the linear dependence of the heat capacity and the existence of zero sound are properties of the Fermi liquid ground state. We also compute the two-point function of the currents at vanishing frequency but do not find any singularities at finite values of the momentum.

Motivated by the recent HAL QCD lattice results on the D - D^* potential at nearly physical point m_π=146.4 MeV, we theoretically examine effects from the two-pion exchange in (semi-)long-range parts of the DD^* system. We employ the framework of heavy-meson chiral perturbation theory with heavy-quark spin symmetry. The pion exchanges up to next-to-next-to-leading order (N^2LO) are taken into account. In order to separate the (semi-)long-range contributions, we apply the dispersion-relation method to one-loop diagrams. As a result, we find that the lattice data on the D - D^* potential in the regime of 0.5, {rm fm} lesssim r is reproduced by adjusting the unknown O(p^2) couplings. In particular, it turns out that contributions from isospin-independent N^2LO triangle diagrams play a central role in reproducing the lattice data of the form V^{DD^*}sim left({rm e}^{-m_πr}/rright)^2 in 1.0, {rm fm} lesssim rlesssim 2.0, {rm fm}. We also present predictions of other D^{(*)} - D^{(*)} potentials, where the similar two-pion exchange tail is predicted. Our findings provide useful information on the (semi-)long-range regime of the D - D^* potential focusing on two-pion exchanges.

Chirality plays an important role in many optical phenomena, and it is crucial to have efficient and accurate numerical algorithms to simulate solutions in this setting. In this paper, we discuss a High-Order Spectral method coupled to geometric regular perturbation theory, which results in just such a method. We view the chirality of the laterally periodic, constant permittivity/permeability structure as deviating from a background value, and demonstrate analyticity of the field scattered by a plane electromagnetic wave with respect to this deformation. This analyticity is not only with respect to chirality deformations of arbitrarily large real size, but also joint in the spatial variables. We also show how the High--Order Perturbation of Envelopes (HOPE) recursions, which we used to establish these results, can be implemented as a rapid, robust, and reliable numerical algorithm.

We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by a Z_N symmetry acting (possibly) non-geometrically on K3. We show that most of these models (in particular, for geometric symmetries) are self-dual under a weak-strong duality acting on the heterotic axio-dilaton modulus S by a "Fricke involution" S --> -1/NS. This is a novel symmetry of CHL models that lies outside of the standard SL(2,Z)-symmetry of the parent theory, heterotic strings on T^6. For self-dual models this implies that the lattice of purely electric charges is N-modular, i.e. isometric to its dual up to a rescaling of its quadratic form by N. We verify this prediction by determining the lattices of electric and magnetic charges in all relevant examples. We also calculate certain BPS-saturated couplings and verify that they are invariant under the Fricke S-duality. For CHL models that are not self-dual, the strong coupling limit is dual to type IIA compactified on T^6/Z_N, for some Z_N-symmetry preserving half of the spacetime supersymmetries.

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a crucial role in hadron physics. For example, theory indicates that the appearance of such correlations is a necessary consequence of dynamical chiral symmetry breaking, viz. a corollary of emergent hadronic mass that is responsible for almost all visible mass in the universe; experiment has uncovered signals for such correlations in the flavour-separation of the proton's electromagnetic form factors; and phenomenology suggests that diquark correlations might be critical to the formation of exotic tetra- and penta-quark hadrons. A broad spectrum of such information is evaluated herein, with a view to consolidating the facts and therefrom moving toward a coherent, unified picture of hadron structure and the role that diquark correlations might play.

We explore the potential of reactor antineutrino-induced Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) data from the CONUS+ experiment to investigate both the Standard Model (SM) and Beyond Standard Model (BSM) scenarios. Alongside CEνNS, Elastic Neutrino-Electron Scattering (EνES) events are also included in our analysis, enabling more stringent constraints on new physics. Within the SM, we examine the weak mixing angle as a precision test of the electroweak sector. For BSM scenarios, we constrain the parameter space of light mediators arising from neutrino generalized interactions (NGI), while also setting limits on the electromagnetic properties of neutrinos, including their charge radius, millicharge, and magnetic moment.

In an earlier paper [arXiv:2511.03669] we extracted the OPE of celestial CFT operator duals of positive helicity graviton and scalar particles from the Mellin transformed relevant MHV amplitudes of conformal gravity, realised as the bosonic subsector of the Berkovits-Witten theory. A soft theorem analysis of bulk MHV amplitudes established that this conformal gravity exhibits a chiral bms_4 symmetry on the celestial sphere with the associated sl(2,R) current algebra, which acquires a non-trivial central extension, unlike the Einstein gravity. Here we construct a 2d chiral CFT free-field realisation of the relevant chiral bms_4 algebra in terms of three free scalars (ϕ_i) and three (β_i,γ_i) ghost pairs, and propose vertex operators for the positive-helicity graviton primary G^{++}_Δ(z,z) as well as the scalar primary Φ_Δ(z,z), and compute their OPEs. These OPEs reproduce exactly those obtained from the bulk conformal gravity MHV amplitudes, providing a concrete celestial dual description of its MHV sector.

Coexistent phase of kaon condensates and hyperons [(Y+K) phase] in beta equilibrium with electrons and muons is investigated as a possible form of dense hadronic phase with multi-strangeness. The effective chiral Lagrangian for kaon-baryon and kaon-kaon interactions is utilized within chiral symmetry approach in combination with the interaction model between baryons. For the baryon-baryon interactions, we adopt the minimal relativistic mean-field theory with exchange of scalar mesons and vector mesons between baryons without including the nonlinear self-interacting meson field terms. In addition, the universal three-baryon repulsion and the phenomenological three-nucleon attraction are introduced as density-dependent effective two-body potentials. The repulsive effects leading to stiff equation of state at high densities consist of both the two-baryon repulsion via the vector-meson exchange and the universal three-baryon repulsion. Interplay of kaon condensates with hyperons through chiral dynamics in dense matter is clarified, and resulting onset mechanisms of kaon condensation in hyperon-mixed matter and the equation of state with the (Y+K) phase and characteristic features of the system are presented. It is shown that the slope L of the symmetry energy controls the two-baryon repulsion beyond the saturation density and resulting stiffness of the equation of state. The stiffness of the equation of state in turn controls admixture of hyperons and the onset and development of kaon condensates as a result of competing effect between kaon condensates and hyperons. The equation of state with the (Y+K) phase becomes stiff enough to be consistent with recent observations of massive neutron stars. Static properties of neutron stars with the (Y+K) phase are discussed.

Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.

According to the generally accepted phase diagram of QCD, at low temperature and high baryon number density the chiral phase transition of QCD is of first order and the co-existence of the Nambu-Goldstone phase and the Wigner phase should appear. This is in conflict with the usual claim that the quark gap equation has no Wigner solution in the case of nonzero current quark mass. In this paper we analyze the reason why the Wigner solution does not exist in the usual treatment and try to propose a new approach to discuss this question. As a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the Wigner solution at finite current quark mass. We then generalize this approach to the case of finite chemical potential and discuss partial restoration of chiral symmetry at finite chemical potential and compare our results with those in the normal NJL model.

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature (T). In this paper we study how this excitation is modified at finite chemical potential (μ). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as Tgtrsim μ.

We demonstrate a universal mechanism of a class of instabilities in infrared regions for massless Abelian p-form gauge theories with topological interactions, which we call generalized chiral instabilities. Such instabilities occur in the presence of initial electric fields for the p-form gauge fields. We show that the dynamically generated magnetic fields tend to decrease the initial electric fields and result in configurations with linking numbers, which can be characterized by non-invertible global symmetries. The so-called chiral plasma instability and instabilities of the axion electrodynamics and (4+1)-dimensional Maxwell-Chern-Simons theory in electric fields can be described by the generalized chiral instabilities in a unified manner. We also illustrate this mechanism in the (2+1)-dimensional Goldstone-Maxwell model in electric field.

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) wormhole in the parity sector that pairs axial metric perturbations with polar gauge perturbations. It contains the axial gravitational mode and the electric field along the magnetic field lines. The lowest Landau level (LLL) of the charged fermions responds through its charge. The gauge components a_τ, a_ρ form a two-dimensional gauge field on the worldsheet of each field line, and the fermions respond with the exact Schwinger current. Lifted over the sphere, it gives the electric field the MMP screening mass m_S^2=αq^2, which is not small and survives in the mouth. In the throat the perturbation tilts the worldsheets, and the Casimir stress tensor acquires mixed components. Force balance then requires a current across the field lines, and charge conservation fixes an accompanying polarisation current, the counterpart of the Hall current of the polar sector. These currents close the Bianchi identities at first order in the fermionic backreaction α. The system reduces to three coupled master equations, given in closed form and matched to the fermion-free mouth. Consistency alone does not select the fermionic constitutive relation, but locality, covariance and the index theorem do. At α=0 the throat reduces to Poschl-Teller problems with masses l(l-1) and (l+1)(l+2) at m_S^2=0. At finite m_S^2 one mode is screened, one tends to the mass l^2+l+2, and one neutral charge-density wave stays exactly massless. The O(α) shifts of the massive normal frequencies are real and negative. The two parity sectors are isospectral only without fermions. The neutral channel sees an attractive region in each mouth, and a numerical solution coupled to the gravitational channel in the exact mouth potential finds no bound state. The sector has no growing mode for lge2 at this order.

In a low-energy effective field theory (EFT), scaling logarithmic terms arise from the renormalization of higher-dimensional couplings that absorb divergences generated by loop integrals with lower-order vertices. Consequently, leading logarithms (LLs) are generated entirely by the leading-order Lagrangian, rendering them universal low-energy predictions. Adapting techniques developed for chiral perturbation theory, we analyze the series of LLs in the EFT of general relativity. As a concrete application, we compute LL corrections to the scalar pole mass up to three-loop order and demonstrate that they can be determined recursively to arbitrary loop order. To confirm the physical validity of our results, we carry out the calculation using a general gauge-fixing parameter and explicitly verify its complete cancellation in the physical observable.

Quantum liquids are characterized by the distinctive properties such as the low temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by L. D. Landau in 1957 and subsequently observed in liquid He-3. In this paper, we ask a question whether such a characteristic behavior is present in theories with holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in AdS_{p+1} space. An example of such a system is the N=4 SU(N_c) supersymmetric Yang-Mills theory with N_f massless N=2 hypermultiplets at strong coupling, finite baryon number density, and low temperature. We find that these systems exhibit a zero sound mode despite having a non-Fermi liquid type behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquids.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with 2Δ, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at t=0 its oscillations decay algebraically as 1/t. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge 2Δ_g, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as 1/t.

Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin-orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk-boundary correspondence giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and of Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss some of the exotic optical and magnetic responses observed in these materials, as well as the progress in developing some of the related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl-line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities.