Chiral Gauge Theories as the Last Frontier of Lattice Fermions

• Hitoshi Murayama (Berkeley / Kavli IPMU)

Room: Panasonic Auditorium, Yukawa Hall Lattice fermions are now highly successful in describing dynamical degrees of freedom in gauge theories, in particular for precise predictions on the hadron spectra or muon anomalous magnetic moment. Yet chiral gauge theories are still at the frontier. So far, the only ideas about dynamics of chiral gauge theories have been the tumbling hypothesis, which postulates the non-perturbative dynamics of a chiral gauge theory keeps breaking itself until it becomes vector-like, a rather strange conjecture. I propose a new methodology to exactly and analytically solve the dynamics of gauge theories by first studying the supersymmetric versions, and breaking supersymmetry slightly by anomaly mediation. I demonstrate evidence that the gauge theory dynamics with slightly broken supersymmetry and no supersymmetry are continuously connected with the same universality class in many cases. Based on this method, chiral gauge theories show different dynamics from the tumbling hypothesis. I hope further developments on lattice fermions will determine which hypothesis is correct.

Regulated chiral gauge theory and the strong CP problem

• Srimoyee Sen (Iowa State University)

Room: Panasonic Auditorium, Yukawa Hall Abstract: Four-dimensional chiral gauge theory can be formulated as the boundary theory on a five-dimensional manifold in a manner that may be realized on a finite lattice. There are interesting features of these theories which defy a purely four-dimensional conception of universality. We find that QCD when embedded in a chiral gauge theory (the Standard Model) and regulated this way appears to suffer neither from a axial U(1) problem nor a strong CP problem, with a central role played by fermion zeromodes localized far away in the fifth dimension. In this way it differs from conventional lattice QCD formulated as a stand-alone theory. Our analysis builds on recent work by others that highlights the role of global U(1) symmetries in five dimensional formulations of four-dimensional chiral gauge theories, and the generic appearance of fermion zeromodes in the bulk.

Constraints on the symmetric mass generation approach to lattice chiral gauge theories

• Yigal shamir (Tel Aviv University)

Room: Panasonic Auditorium, Yukawa Hall It is difficult to reconcile chiral symmetry with the lattice because of the fermion doubling problem. I start by explaining why simple solutions, that work for the global chiral symmetry of QCD, fail in the case of a chiral gauge theory. I will then introduce the "symmetric mass generation", or SMG, paradigm, which aims to decouple the fermion doublers by introducing judiciously chosen mutli-fermion or fermion-scalar interactions. The main result I will present is a generalization of the Nielsen-Ninomiya "no-go" theorem, which is a theorem about free lattice hamiltonians, to interacting (including SMG) models. The physical reasons why such a generalization exists will be clarified, as well as the conditions of the generalized theorem. This in turn leads to a "check list" that should be addressed in any SMG model if it is to succeed in generating a lattice chiral gauge theory in the continuum limit. As a testbed, I will discuss recent efforts to put on the lattice the so-called 3-4-5-0 chiral Schwinger model. Time permitting, I will also briefly discuss other approaches to the construction of lattice chiral gauge theories that have obtained partial successes, but also have remaining open issues.

Exact $\mathrm{SL}(2,\mathbb{Z})$-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation

• Shoto Aoki (RIKEN iTHEMS)

Room: Panasonic Auditorium, Yukawa Hall We study the duality of lattice Maxwell theory in the modified Villain formulation, employing an ultra-local action with a theta term. Although this action is known to become non ultra-local through the Poisson resummation formula, we show that this non ultra-locality can be removed by incorporating a non-local transformation procedure into the definition of the $\mathcal{S}$-transformation. As a result, the ultra-local action with a theta term exhibits an exact $\mathrm{SL}(2,\mathbb{Z})$-duality. We further analyze the $\mathrm{SL}(2,\mathbb{Z})$-structure of Wilson and ’t Hooft loops, demonstrating that they transform properly up to a nontrivial phase factor arising from the nontrivial self-linking of the loops. This effect originates from the non-local transformation procedure in the $\mathcal{S}$-transformation. Remarkably, the resulting $\mathrm{SL}(2,\mathbb{Z})$-structure closely resembles that of non-spin Maxwell theory.

Lattice chiral symmetry from bosons in 3+1d

• Shu-Heng Shao (Massachusetts Institute of Technology)

Room: Panasonic Auditorium, Yukawa Hall We present an explicit Hamiltonian that realizes an exact lattice chiral U(1)_V x U(1)_A recently proposed. Nielsen-Ninomiya-type no-go theorems are evaded by using lattice bosons rather than fermions. The continuum limit is a compact boson field theory with an axion-like coupling. While U(1)_V shifts the lattice scalar, U(1)_A acts on short axion string excitations. We demonstrate the chiral anomaly by showing that U(1)_A is broken when U(1)_V is gauged. Finally, gauging either U(1)_V and U(1)_A leads to lattice non-invertible and 2-group symmetries, respectively.

On the Hamiltonian formalism of Spin(10) chiral lattice gauge theory

• Yoshio Kikukawa (University of Tokyo)

Room: Panasonic Auditorium, Yukawa Hall We first discuss the reflection positivity in the path-integral formalism of Spin(10) chiral lattice gauge theory with overlap Weyl fermions, where the fermion path-integral measure is formulated by the complete saturation of ’t Hooft vertecies in right-handed components. We next examine the relation of domain-wall fermion in Hamilotnian formalism to Creutz-Horvath-Neuberger (CHN) Dirac fermion and discuss how to obtain the Weyl fermion degrees of freedom out of CHN Dirac fermion

Conditions for Symmetric Mass Generation in Lattice-QCD

• Cenke Xu (University of California, Santa Barbara)

Room: Panasonic Auditorium, Yukawa Hall We first review the basic concept, necessary conditions, and well-known examples of symmetric mass generation. Then we will apply these general ideas to lattice-QCD, focusing on the staggered fermions. We also discuss the current status of the efforts of observing SMG in lattice-QCD.

Lieb-Schultz-Mattis anomaly in dissipative Majorana chains

• Tokiro Numasawa (The University of Tokyo)

Room: Panasonic Auditorium, Yukawa Hall We study the Lieb-Schultz-Mattis anomaly in Majorana chains with dissipation. In Hamiltonian systems, Majorana translations flow to chiral fermion parity symmetries in the continuum limit. In this talk, we investigate the relation between Majorana translations and chiral fermion parity in open quantum systems. We present an anomaly among weak and strong symmetries that is peculiar to open Majorana chain models. We also present a concrete quantum master equation (Lindblad equation) with strong Majorana translation symmetry and the effects of anomalies on the spectrum of the Liuville operators.

Lattice Dirac operators and K-theory

• Hidenori Fukaya (Osaka Univ.)

Room: Panasonic Auditorium, Yukawa Hall We employ $K$-theory to classify the Wilson Dirac operators to study gauge field topology on the lattice. In contrast to the index of the overlap Dirac operator defined through the Ginsparg-Wilson relation, which is restricted to flat tori in even dimensions, our formulation offers several key advantages: 1) It can be applied straightforwardly to the Atiyah-Patodi-Singer index for manifolds with boundary. 2) The boundary can be curved, allowing for the inclusion of gravitational background effects. 3) The mod-2 index in both even and odd dimensions can be defined as a natural extension of the same formulation. In this talk, we present the mathematical proof and provide numerical evidence supporting the formulation.

Exact Chiral Symmetry with Quantum Signal Processing

• Hersh Singh (Fermilab)

Room: Panasonic Auditorium, Yukawa Hall We study quantum simulation algorithms for two formulations of Hamiltonian lattice fermions with an exact chiral symmetry based on the domain-wall and overlap formulations. We present a quantum simulation algorithm based on Quantum Signal Processing (QSP), which optimally preserves the Ginsparg-Wilson (GW) relation and therefore the chiral symmetry. We show how QSP effectively constructs an extra dimension when simulating the overlap operator, showing how studying the scaling of quantum algorithms reflects the deeper physical connection between overlap fermions arising as the boundary theory of domain-wall fermions.

A qubit-based framework for quantum simulations of curved-spacetime quantum field theories

• Daisuke Yamamoto (CHS, Nihon University)

Room: Panasonic Auditorium, Yukawa Hall We propose a qubit-based framework for quantum simulations of quantum field theories in curved spacetimes using quantum spin systems. Starting from a spin-1/2 Hamiltonian with spatially and temporally varying exchange couplings and magnetic fields, we first map the system through the Jordan-Wigner transformation to a lattice Hamiltonian of Majorana fermions. Taking the continuum limit, the lattice fermion model reproduces Majorana quantum field theories on general two-dimensional curved spacetimes. This establishes a direct correspondence between spacetime geometry and experimentally controllable parameters in quantum devices, while naturally connecting qubit systems and Hamiltonian lattice-fermion formulations of curved-spacetime quantum field theories. Using this framework, we study several gravitational quantum phenomena, including particle production in expanding universes described by Friedmann-Lemaître-Robertson-Walker spacetimes, quantum field dynamics in de Sitter spacetimes, and black-hole physics such as Hawking radiation. These examples demonstrate that qubit-based quantum simulators can provide a versatile platform for investigating nonequilibrium quantum phenomena associated with curved spacetimes and horizons. Our framework opens a route toward “tabletop universe” simulations of gravitational quantum phenomena using near-term quantum devices.

Higher-form anomalies on lattices (for bosons and fermions)

• Ryohei Kobayashi (University of Tokyo)

Room: Panasonic Auditorium, Yukawa Hall I will talk about a way to characterize anomalies of higher-form symmetries in lattice models. I also plan to mention higher-form anomalies intrinsic in (2+1)D fermionic systems and their lattice realizations, based on an ongoing work with Matthew Yu.

Fermions and Zeta Function on the Graph

• Kazutoshi Ohta (Meiji Gakuin University)

Room: Panasonic Auditorium, Yukawa Hall We propose a construction of fermions on arbitrary graphs, regarded as discrete space-time. In our framework, the Dirac operator for fermions on the graph is formulated in terms of an incidence matrix deformed by specific parameters. Consequently, the partition function of the model is given by the inverse of the graph zeta function (Ihara zeta function). We explore the physical significance of the graph zeta function, showing that it provides a generating function for the possible fermion cycles (states) on the graph. Furthermore, utilizing concepts such as covering graphs and Artin-Ihara $L$-functions, we analyze fermions on lattices (grid graphs) with periodic boundary conditions and demonstrate that the fermion-doubling problem is avoided in our construction. Additionally, we reveal a significant connection between the partition function of this model and that of the Ising model by introducing winding numbers associated with graph cycles. Finally, we examine the index theorem applicable to graphs within our framework. (This talk is based on https://arxiv.org/abs/2501.08803 .)

Chiral Gauge Theories from Symmetry Disentanglers

• Ryan Thorngren (UCLA)

Room: Panasonic Auditorium, Yukawa Hall We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on- site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice ro- tor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for U (1) symmetries with mixed ’t Hooft anomalies, and show that sym- metry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional “3450” chiral gauge theory, and we argue that a related construction applies to the U (1) hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories. This talk is based on our article https://arxiv.org/abs/2601.04304 with Lukasz Fidkowski and John Preskill.

Exact Chiral Symmetries of 3+1⁢D Hamiltonian Lattice Fermions

• Lei Gioia Yang (California Institute of Technology)

Room: Panasonic Auditorium, Yukawa Hall We construct Hamiltonian models on a 3+1⁢D cubic lattice for a single Weyl fermion and for a single Weyl doublet protected by exact (as opposed to emergent) chiral symmetries. In the former, we find a not-on-site, noncompact chiral symmetry which can be viewed as a Hamiltonian analog of the Ginsparg-Wilson symmetry in Euclidean lattice models of Weyl fermions. In the latter, we combine an on-site U(1) symmetry with a not-on-site U(1) symmetry, which together generate the SU(2) flavor symmetry of the doublet at low energies, while in the UV they generate an algebra known in integrability as the Onsager algebra. This latter model is in fact the celebrated magnetic Weyl semimetal, which is known to have a chiral anomaly from the action of U(1) and crystalline translation. This anomaly gives rise to an anomalous Hall response; however, when reinterpreted in our language, the model has two exact U(1) symmetries that give rise to the global SU(2) anomaly, which protects the gaplessness even when crystalline translations are broken. We also construct an exact symmetry-protected single Dirac cone in 2+1⁢D with the U⁡(1) ⋊𝑇 parity anomaly. Our constructions evade both old and recently proven no-go theorems by using not-on-siteness in a crucial way, showing our results are sharp.

A new approach to formulating chiral gauge theory on the lattice

• vatsalya vaibhav (Higgs Centre for Theoretical Physics, University of Edinburgh)

Room: Panasonic Auditorium, Yukawa Hall We propose a way to formulate a realistic chiral gauge theory like the standard model on a lattice (or a general simplicial complex in curved spacetime), so that it has the correct continuum limit, with the correct symmetries and (co)homological properties, and no unwanted doublers or anomalies. Building on recent ideas of Catterall and collaborators, our approach uses restricted Kahler-Dirac fermions (spinors with a dual interpretation as differential forms). To obtain the right continuum limit, we find we must appropriately couple the Kahler-Dirac fermions to the tetrad and spin connection one-forms (which describe the geometry of spacetime). Conceptually, the crucial new point in our formulation is to carefully distinguish between the diffeomorphism group (which is broken by discretization) and the local Lorentz group (which is exactly preserved). (In collaboration with Latham Boyle.)

Lattice 2D $U(1)$ chiral gauge theory and magnetically charged vertex operators via bosonization

• Okuto Morikawa (RIKEN)

Room: Panasonic Auditorium, Yukawa Hall Two-dimensional Abelian chiral gauge theories provide a useful setting for studying the interplay between gauge invariance, locality, and anomalies on the lattice. In this talk, I will discuss a lattice formulation of 2D $U(1)$ chiral gauge theory based on bosonization, with particular emphasis on magnetically charged vertex operators. In the bosonized description, charged fermionic operators are represented by vertex operators of scalar fields. The corresponding dual vertex operators carry magnetic charge and therefore require a careful lattice definition. I will explain how such operators can be realized geometrically by excising small regions from the lattice, so that an operator insertion is represented as a hole. This construction gives a concrete way to define charged operators while preserving exact gauge invariance for anomaly-free fermion contents. I will also discuss how anomaly cancellation is reflected in the bosonized lattice theory and what this viewpoint suggests for lattice approaches to chiral gauge theories and anomalies.

Symmetric mass generation of 8 Majorana domain-wall fermions

• Sho Araki (Osaka university)

Room: Panasonic Auditorium, Yukawa Hall Symmetric mass generation (SMG) is a mechanism for opening a gap without spontaneous breaking of symmetry, which was first shown in the 1-dimensional Maojorana chain model by Fidkowski and Kitaev(FK). We consider the path-integral of the FK model on a 2-dimensional lattice with and without domain-walls. We numerically show that the $Z_8$ structure is properly encoded in the Majorana fermion pfaffian and a preliminary evidence that we can gap out one of the edge-localized modes on two domain-walls by 4-Fermi interactions. This talk is based on arXiv:2512.11424 and a work in progress.

Exotic theta terms in 2+1d fractonic field theory

• Yuki Furukawa (University of Tokyo)

Room: Panasonic Auditorium, Yukawa Hall In this work, we study exotic theta terms in the 2+1d $\phi$-theory, which provides a continuum description of the XY-plaquette model. The $\phi$-theory can be viewed as a fractonic analogue of the 1+1d compact boson and exhibits momentum and winding subsystem symmetries. In this theory, discontinuous field configurations play a crucial role. Although such configurations spoil the naive topology of the field, they induce nontrivial backreactions that give rise to new topological terms. We study two types of theta terms, which we call the bulk theta term and the foliated theta term. The foliated theta term is constructed by coupling winding currents on neighboring leaves of a foliation. Remarkably, the corresponding theta angle can vary spatially without affecting the classical equations of motion. Both theta terms lead to generalized Witten effects, in which vortex operators carrying winding subsystem charge acquire momentum subsystem charge. In the case of the foliated theta angle, the Witten effect exhibits a more intricate structure: vortex operators acquire a quadrupolar momentum charge. We demonstrate these features using lattice realizations based on the modified Villain formulation. This talk is based on arXiv:2604.07293.

Reducing the residual mass of domain-wall fermions using machine learning

• Shunsuke Yasunaga (Institute of Science Tokyo)

Room: Panasonic Auditorium, Yukawa Hall Domain-wall fermions provide a good lattice realization of chiral fermions by introducing an additional fifth dimension. At finite fifth-dimensional extent, residual chiral symmetry breaking remains and is characterized by the residual mass. We propose a machine-learning-based parameter-optimization approach to reduce the residual mass while keeping the fifth dimension short. This method aims to emulate the effect of a longer fifth dimension through optimized domain-wall fermion parameters, thereby improving chiral symmetry without significantly increasing the computational cost.

Confinement without dynamical symmetry breaking in chiral gauge theories

• Alvaro Pastor Gutierrez (RIKEN iTHEMS)

Room: Panasonic Auditorium, Yukawa Hall The infrared structure of gauge theories with chiral fermions remains largely unexplored. In this talk I will investigate the Bars-Yankielowicz class using the functional renormalisation group, building on recent developments in gauge-fermion systems that provide clear criteria for confinement and dynamical symmetry breaking. We show that two distinct phases arise: one exhibiting both confinement and symmetry breaking at small numbers of colours, and another characterised by confinement without symmetry breaking in the large-colour limit. The latter realises a novel regime, opening the possibility of exotic spectra and phenomena that can now be studied within a systematic framework.

Violation of Parity and Flavor Symmetries in a Nambu-Jona-Lasinio Model

• Yukimi Goto (東京大学)

Room: Panasonic Auditorium, Yukawa Hall In this talk, I discuss a lattice Nambu–Jona-Lasinio model with certain continuous chiral and two-flavor symmetries. For the Hamiltonian of this model, we construct a ground state that simultaneously breaks parity and flavor symmetries. This phase structure may be viewed as analogous to the Aoki phase, although the model does not contain a Wilson term.

Taste-splitting mass and bulk-boundary correspondence in 3+1D staggered fermions

• Tatsuya Yamaoka (The University of Osaka)

Room: Panasonic Auditorium, Yukawa Hall We discuss taste-splitting mass terms and their symmetries in the 3+1 dimensional staggered fermion system, and show that the one-link mass term in the x-direction preserves the largest symmetry. Using this mass term, we construct a 2+1 dimensional boundary theory and demonstrate that the flavor SU(2) symmetry and parity anomaly of the boundary theory are reproduced by the conserved charges generating the Onsager algebra on the 3+1 dimensional bulk lattice.

Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling

• Vladimir Zakharov (Lorentz Institute, Leiden University)

Room: Panasonic Auditorium, Yukawa Hall Massless chiral fermions can become massive without spontaneous symmetry breaking for a special class of “anomaly-free” interactions. This phenomenon of “symmetric mass generation” (SMG) has been demonstrated numerically on a two-dimensional lattice, for a local discretization with a sine dispersion that doubles the fermion number. Here we demonstrate the effect on a one-dimensional lattice, avoiding the fermion-doubling obstruction by means of a nonlocal discretization that replaces the sine by a tangent. The gapping interaction in the anomaly-free 3–4–5–0 model of Wang and Wen is perturbatively irrelevant, preventing a weak-coupling analysis of the numerical data. We work around this difficulty by including a Hubbard interaction that makes the gapping interaction relevant for Luttinger parameter K < 2/5 ≡ K_c. This makes it possible to stay in the weak coupling regime where SMG can be well described by a scaling analysis. We observe the opening of an excitation gap once K drops below K_c, while the ground state remains nondegenerate — hallmark of the SMG transition.

Monopole scattering, Unitarity Puzzle, and Symmetric mass generation

• Atsushi Ueda (Ghent University)

Room: Panasonic Auditorium, Yukawa Hall What happens when a charged chiral fermion interacts with a monopole? This fundamental question has arisen within the standard model. Callan discovered that what bounces back is not the original fermion but rather a particle that sometimes has a fractional charge, suggesting a fraction of electrons. This paradox, known as the "monopole paradox," has long posed interpretative challenges. Recently, a series of works have made progress on this topic, showing that the scattered particle can be viewed as a chiral fermion dressed with a topological string attached to the monopole. This string brings the fermion into the twisted sector, resulting in a fractional charge. This serves as a compelling example in field theory. But what about on the lattice? In this talk, I will introduce analogous cases in condensed matter physics. When a pair of dual theories is coupled, we can design the interaction at the interface that exhibits perfect transmission for any wave packet. The particle that passes through the interface appears quite different from the original, as it is essentially disguised by a topological line. I will demonstrate a generic yet straightforward method to construct these models using matrix product unitaries and conclude by discussing the implications for some applications and the monopole paradox.