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Chiral edge states on spheres for lattice domain wall fermions
Recently Weyl edge states on manifolds in dimension 𝑑 +1 with a connected 𝑑-dimensional boundary were proposed as candidates for lattice regularization of chiral gauge theories, for even 𝑑. The examples considered to date include solid cylinders in any odd dimension, and the 3 ball with boundary 𝑆 2 . Here we consider the general case of a (𝑑+1)-dimensional ball for any even 𝑑 and show that the theory for the edge states on 𝑆 𝑑 describe a conventional Weyl fermion on a sphere with half-integer momenta. A possible advantage of such theories is that they can be discretized by a square lattice without breaking the underlying discrete hypercubic symmetry.
Parity-Violating Møller Scattering at Next-to-Next-to-Leading Order: Closed Fermion Loops
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Continuous symmetry breaking in a two-dimensional Rydberg array
Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. In conclusion, our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry.
One dimensional staggered bosons, clock models, and their noninvertible symmetries
We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete Z N symmetry predict that these are critical points with a U ( 1 ) current algebra at c = 1 and radius 2 N whenever N > 4 . We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024
Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice
The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.
Filling constraints on translation invariant dipole conserving systems
Systems with conserved dipole moment have drawn considerable interest in light of their realization in recent experiments on tilted optical lattices. Here, an important question for such systems is delineating the conditions under which they admit a unique gapped ground state that is consistent with all symmetries. Here, we study one-dimensional translation-invariant lattices that conserve U(1) charge and Z L dipole moment, where discreteness of the dipole symmetry is enforced by periodic boundary conditions, with L the system size. We show that in these systems, a symmetric, gapped, and non-degenerate ground state requires not only integer charge filling, but also a fixed value of the dipole filling, while other fractional dipole fillings enforce either a gapless or symmetry-breaking ground state. In contrast with prior results in the literature, we find that the dipole filling constraint depends both on the charge filling as well as the system size, emphasizing the subtle interplay of dipole symmetry with boundary conditions. We support our results with numerical simulations and exact results.
Generalized symmetry constraints on deformed 4D SCFTs
We explore the consequence of generalized symmetries in four-dimensional N = 1 superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the Adler-Bell-Jackiw (ABJ) anomaly, we find that many of these theories have mixed zero-form or one-form ’t Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two D 3 ( S U ( N ) ) theories and S U ( N ) gauge theory with two adjoints. We also repeat our analysis for a host of nonsupersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs. Published by the American Physical Society 2025
A thermodynamically consistent discretization of 1D thermal-fluid models using their metriplectic 4-bracket structure
Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this modeling formalism to preserve thermodynamic consistency in discretizations of a fluid model. The procedure relies (1) on ensuring that the spatial semi-discretization retains certain symmetries and degeneracies of the Poisson and metriplectic 4-brackets, and (2) on the use of an appropriate energy conserving time-stepping method. Here, the minimally simple yet nontrivial example of a one-dimensional thermal-fluid model is treated. It is found that preservation of the requisite symmetries and degeneracies of the 4-bracket is relatively simple to ensure in Galerkin spatial discretizations, suggesting a path forward for thermodynamically consistent discretizations of more complex fluid models using more specialized Galerkin methods.
High-quality axion from exact SUSY chiral dynamics
We use supersymmetric chiral dynamics perturbed by anomaly-mediated supersymmetry breaking to obtain a high-quality, composite axion that solves the strong problem. The strong dynamics arises from a supersymmetric SU(10) chiral gauge theory with massless matter chiral superfields. This leads to a stable, nonsupersymmetric vacuum, calculated exactly, where a spontaneously broken global symmetry, identified with the Peccei-Quinn (PQ) symmetry, gives rise to a composite QCD axion. The chiral gauge theory also admits a discrete (or ) gauge symmetry that forbids PQ-violating operators up to dimension eight. An extension to an chiral gauge theory incorporates grand unification where the unification scale is identified with the PQ-breaking scale and PQ-violating operators are forbidden up to dimension 20. The supersymmetry breaking scale, near 100 TeV, ameliorates the Higgs hierarchy problem, while colored Nambu–Goldstone bosons may be detected at future colliders via decays to gluons or form heavy isotopes.
Entanglement maximization and mirror symmetry in two-Higgs-doublet models
We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets Φ a , a = 1, 2, can be viewed as a qubit: Φ 1 = |0⟩ and Φ 2 = |1⟩. More specifically, we compute the scattering amplitudes for Φ a Φ b → Φ c Φ d and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of {|00⟩, |01⟩, |10⟩, |11⟩}. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an U(2) × U(2) global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact U(2) × U(2) symmetry, which is spontaneously broken to U(1) × U(1). As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The U(2) × U(2) symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete Z 2 symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the Z 2 symmetry.
A low-scale flavon model with a $ {\mathrm{\mathbb{Z}}}_N$ symmetry
We propose a model that explains the fermion mass hierarchy by the Froggatt-Nielsen mechanism with a discrete $ {\mathrm{\mathbb{Z}}}_N^F $ symmetry. As a concrete model, we study a super-symmetric model with a single flavon coupled to the minimal supersymmetric Standard Model. Flavon develops a TeV scale vacuum expectation value for realizing flavor hierarchy, an appropriate μ -term and the electroweak scale, hence the model has a low cutoff scale. We demonstrate how the flavon is successfully stabilized together with the Higgs bosons in the model. The discrete flavor symmetry $ {\mathrm{\mathbb{Z}}}_N^F $ controls not only the Standard Model fermion masses, but also the Higgs potential and a mass of the Higgsino which is a good candidate for dark matter. The hierarchy in the Higgs-flavon sector is determined in order to make the model anomaly-free and realize a stable electroweak vacuum. We show that this model can explain the fermion mass hierarchy, realistic Higgs-flavon potential and thermally produced dark matter at the same time. We discuss flavor violating processes induced by the light flavon which would be detected in future experiments.
Rotational symmetry protected edge and corner states in Abelian topological phases
Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.
Minimal dark 𝑆𝑈(2) origin of a massless Dirac neutrino
We propose a gauge-symmetry origin of a rank-two Dirac neutrino mass matrix that enforces one exactly massless neutrino, while being consistent with the oscillation data, as well as cosmological constraints. The mechanism relies on a minimal dark 𝑆𝑈(2) 𝐷 gauge symmetry under which one right-handed neutrinolike Weyl fermion is charged, thereby forbidding its Standard Model Yukawa coupling. Quantum consistency then fixes the minimal dark-sector completion: Cancellation of the Witten anomaly requires a second fermionic 𝑆𝑈(2) 𝐷 doublet, while a discrete 𝑍 4 symmetry that forbids Majorana masses allows the two dark doublets to form a vectorlike pair. This anomaly-free completion gives rise to a secluded, confining dark sector that can contain a potential dark matter candidate, linking the protected neutrino texture to dark infrared dynamics.
Scalar-induced neutrinoless double beta decay in SU(5)
We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay (0νββ) within the SU(5) Grand Unified Theory framework, extended suitably to include neutrino mass. In such a minimal realistic SU(5) setup for fermion masses, the scalar contributions to 0νββ are extremely suppressed as a consequence of the proton decay bound. We circumvent this problem by imposing a discrete Z 3 symmetry. However, the scalar contributions to 0νββ remain suppressed in this SU(5) x Z 3 model due to the neutrino mass constraint. We find that the 0νββ contribution can be enhanced by extending the scalar sector with an additional 15-dimensional scalar representation with suitable Z 3 charge. Such an extension not only yields realistic fermion mass spectra but also leads to experimentally testable predictions in upcoming ton-scale 0νββ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to ∼ 10 10 GeV.
Dark matter and dark radiation from the early universe with a modulus coupled to the PQMSSM
The supersymmetrized DFSZ axion model is especially compelling in that it contains 1. the SUSY solution to the gauge hierarchy problem, 2. the Peccei-Quinn (PQ) solution to the strong CP problem and 3. the Kim-Nilles solution to the SUSY μ problem. In a string setting, where a discrete R-symmetry ($Z$$^{R}_{24}$ for example) may emerge from the compactification process, a high-quality accidental axion (accion) can emerge from the accidental, approximate remnant global U(1) PQ symmetry where the decay constant f a is linked to the SUSY breaking scale, and is within the cosmological sweet zone. In this setup, one also expects the presence of stringy remnant moduli fields Φ i . Here, we consider the situation of a single light modulus Φ coupled to the PQMSSM in the early universe, with mixed axion plus higgsino-like WIMP dark matter. We evaluate dark matter and dark radiation production via nine coupled Boltzmann equations and assess the severity of the cosmological moduli problem (CMP) along with dark matter and dark radiation production rates. We find that typically the light modulus mass should be m Φ ≳ 10 4 TeV to avoid the moduli-induced dark matter overproduction problem. If one is able to (anthropically) tune the modulus field amplitude, we find a value of Φ 0 ≲ 10 –7 m P would be required to solve the overall CMP.
Nonperturbative and perturbative dynamics of a light QCD axion: Dark matter and the strong 𝐶𝑃 problem
Considerable theoretical efforts have gone into expanding the reach of the quantum chromodynamics (QCD) axion beyond its canonical mass–decay-constant relation. The 𝑍 𝒩 QCD axion model reduces the QCD axion mass naturally, by invoking a discrete 𝑍 𝒩 symmetry through which the axion field is coupled to 𝒩 copies of the Standard Model. Before the QCD phase transition at temperature 𝑇 QCD , the 𝑍 𝒩 potential has a minimum at misalignment angle 𝜃 = 𝜋. At 𝑇 QCD , 𝜃 = 𝜋 becomes a maximum; the axion potential becomes exponentially suppressed and develops 𝒩 minima—only one of which actually solves the strong 𝐶𝑃 problem. Before 𝑇 QCD , 𝜃 relaxes toward 𝜋. After 𝑇 QCD , the axion field starts from around the hilltop and may have sufficient kinetic energy to overcome the newly suppressed potential barriers. Such a field evolution leads to nonperturbative effects via the self-interactions near the hilltop, which can cause the exponential growth of fluctuations and backreaction on the coherent motion. This behavior can influence the relic density of the field and the minimum in which it settles. We conduct the first lattice simulations of the 𝑍 𝒩 QCD axion using 𝒞osmoℒattice to accurately calculate dark matter abundances and find nonperturbative dynamics reduce the abundance by up to a factor of two. We furthermore find that the probability of solving the strong 𝐶𝑃 problem tends to diverge considerably from the naïve expectation of 1/𝒩.
Sublattice modulated superconductivity in the kagome Hubbard model
Here we identify a superconducting order featuring spatial pair modulations on the kagome lattice subject to onsite Hubbard U and nearest neighbor V interactions. Within our functional renormalization group analysis, this state appears with a concomitant d-wave superconducting (SC) instability at zero lattice momentum, where it distinguishes itself through intra-unit cell modulations of the pairing function thus breaking the discrete space group symmetry. The relative weight of the sublattice modulated superconductor (SMS) and d-wave SC is influenced by the absolute interaction strength and coupling ratio V/U. Parametrically adjacent to this domain at weak coupling, we find an intra-unit cell modulated vestigial charge density wave and an s-wave SC instability. Our study provides a microscopic setting and thorough description of this novel SMS arising within a translation symmetry broken background.