Simulating a chiral gauge theory
Authors: Laurens Lootens, Hersh Singh
Abstract
Chiral gauge theories underlie the Standard Model, yet none has been simulated nonperturbatively. Lattice constructions that evade the Nielsen-Ninomiya obstruction entail complex fermion measures or infinite-dimensional local Hilbert spaces. Here we provide a gauge-invariant Hamiltonian lattice regularization of 1+1-dimensional abelian chiral gauge theories built from clock-and-shift qudits with $\mathbb{Z}_N$ gauge fields, in which the global chiral symmetry and its 't Hooft anomaly survive exactly mod $N$. Anomaly cancellation on the lattice lets the Gauss laws be imposed and solved exactly, reducing the theory to an unconstrained qudit chain. Using infinite matrix product states, we simulate the canonical 1+1-dimensional chiral gauge theory, the 34-50 model, and find excellent agreement with analytic predictions, showing that a finite-dimensional local Hilbert space at $N=6$ reproduces the expected infrared physics of the continuum 34-50 model. This provides an efficient and practical solution to the problem of simulating general abelian chiral gauge theories in 1+1 dimensions, both on classical and quantum computers.
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Solution to the 1+1 dimensional gauged chiral Fermion problemJuven C. Wang, Xiao-Gang Wen · 2018 · Physical Review D · cited 27 times · Not summarized yet
Solution to the 1+1 dimensional gauged chiral Fermion problem constructs a finite-range lattice realization of the 3450 U(1) chiral gauge theory.
Abstract
We show that the 3450 U(1) chiral fermion theory can appear as the low energy effective field theory of a 1+1D local lattice model, with an on-site U(1) symmetry and finite-range interactions. The on-site U(1) symmetry means that the U(1) symmetry can be gauged (gaugeable for both background probe and dynamical fields), which leads to a non-perturbative definition of chiral gauge theory --- a chiral fermion theory coupled to U(1) gauge theory. Our construction can be generalized to regularize any U(1)-anomaly-free 1+1D gauged chiral fermion theory with a zero chiral central charge (thus no gravitational anomaly) by a lattice, thanks to the recently proven "Poincar\'e dual" equivalence betwee…
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A Method for simulating chiral fermions on the latticeD. Kaplan · 1992 · Physics Letters B · cited 972 times · Not summarized yet
A Method for simulating chiral fermions on the lattice introduces extra-dimensional mass defects to realize chiral fermions and explain their anomalies.
Abstract
Abstract I show that a lattice theory of massive interacting fermions in 2 n +1 dimensions may be used to simulate the behavior of massless chiral fermions in 2 n dimensions if the fermion mass has a step function shape in the extra dimension. The massless states arise as zero modes bound to the mass defect, and all doublers can be given large gauge invariant masses. The manner in which the anomalies are realized is transparent: apparent chiral anomalies in the 2 n -dimensional subspace correspond to charge flow into the extra dimension.
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Abelian chiral gauge theories on the lattice with exact gauge invarianceM. Lüscher · 1998 · Nuclear Physics · cited 183 times · Not summarized yet
Abelian chiral gauge theories on the lattice with exact gauge invariance uses the Ginsparg-Wilson relation to construct anomaly-free lattice theories, rather than clock-shift qudits.
Abstract
Abstract It is shown that U(1) chiral gauge theories with anomaly free multiplets of Weyl fermions can be put on the lattice without breaking the gauge invariance or violating any other fundamental principle. The Ginsparg-Wilson relation plays a key role in this construction, which is non-perturbative and includes all topological sectors of the theory in finite volume. In particular, the cancellation of the gauge anomaly and the absence of global topological obstructions can be established on the basis of this relation and the lattice symmetries alone.
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A Note On Lattice Definition of Gauge Theories With Chiral FermionsE. Witten · 2026 · Not summarized yet
A Note On Lattice Definition of Gauge Theories With Chiral Fermions discusses a lattice algorithm for chiral gauge theories, including its practical limitations.
Abstract
Because of the fermion doubling problem, it has been a longstanding challenge to describe a lattice algorithm for studying four-dimensional gauge theories coupled to chiral fermions. Recently, an algorithm to do so has been described by Craig, extending partial results in the previous literature. Here we describe a variant of this algorithm, based on interpolating a lattice gauge field over the continuum (as in Craig's work) and coupling the interpolated gauge field to continuum chiral fermions. The same variant was also proposed recently by Hsu. In any dimension and for any anomaly-free representation, this approach can be implemented on a computer in principle, but not in practice by Monte…
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Lattice chiral non-Abelian gauge symmetry via bosonizationSoma Onoda · 2026 · cited 1 time · Not summarized yet
Lattice chiral non-Abelian gauge symmetry via bosonization formulates a two-dimensional non-Abelian chiral gauge theory using bosonization and anomaly inflow.
Abstract
A central issue in lattice formulations of chiral gauge theories is how the anomaly cancellation mechanism of the continuum theory can be realized at finite lattice spacing. In the present paper, based on non-Abelian bosonization, we propose a lattice formulation of the bosonic theory corresponding to a two-dimensional non-Abelian chiral gauge theory. In the continuum theory, the gauge anomaly of chiral fermions is represented, in the bosonized description, as anomaly inflow from a three-dimensional Chern--Simons-type bulk contribution contained in a gauged Wess--Zumino--Witten model. Motivated by this structure, we introduce gauge-neutral spectator fermions and use the resulting bosonized d…
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Novel Lattice Formulation of 2D Chiral Gauge Theory via BosonizationSoma Onoda, Okuto Morikawa, Hiroshi Suzuki · 2025 · Proceedings of The 41st International Symposium on Lattice Field Theory — PoS(LATTICE2024) · cited 1 time · Not summarized yet
Novel Lattice Formulation of 2D Chiral Gauge Theory via Bosonization proposes an excision-based formulation of two-dimensional Abelian chiral gauge theory.
Abstract
Recently, lattice formulations of 2D Abelian chiral gauge theory have been constructed based on Abelian bosonization. It is remarkable about these 2D lattice formulations that they reproduce the same gauge anomaly structure as the continuum theory, even at a finite lattice spacing. In this talk, we propose yet another lattice formulation based on the ``excision method'' introduced recently in Ref.~\cite{Abe:2023uan}. This approach respects the admissibility condition, which is a constraint on the smoothness of lattice field configurations; it usually prohibits magnetically charged objects, that is, vector-charged objects in fermion theories. We show that such objects can be defined in the ex…
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Exact lattice chiral symmetry in 2D gauge theoryEvan Berkowitz, Aleksey Cherman, Theodore Jacobson · 2023 · Physical Review D · cited 27 times · Not summarized yet
Exact lattice chiral symmetry in 2D gauge theory uses bosonization and modified Villain actions to reproduce anomalies and obtain sign-problem-free dual formulations.
Abstract
We construct symmetry-preserving lattice regularizations of 2D QED with one and two flavors of Dirac fermions, as well as the “3450” chiral gauge theory, by leveraging bosonization and recently proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we find a sign-problem-free dual formulation. Published by the American Physical Society 2024
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Regulated Chiral Gauge Theory and the Strong CP problemDavid B. Kaplan, Srimoyee Sen · 2024 · cited 6 times · Not summarized yet
Regulated Chiral Gauge Theory and the Strong CP problem studies a five-dimensional boundary construction for four-dimensional chiral gauge theory and its implications for QCD.
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 can simultaneously avoid both the $U(1)_A$ problem and the 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, universality being violated by inaccessible light modes in the …
Prior work it builds on
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Exactly Solvable 1+1d Chiral Lattice Gauge TheoriesSahand Seifnashri · 2026 · cited 16 times · Not summarized yet
Exactly Solvable 1+1d Chiral Lattice Gauge Theories constructs an Abelian lattice model of the 34-50 theory, using modified Villain variables and an exactly solvable Hamiltonian.
Abstract
Using the modified Villain lattice Hamiltonian formulation of the 1+1d compact boson theory, we construct exactly solvable abelian chiral lattice gauge theories in two spacetime dimensions. As a concrete example, we derive an explicit quadratic lattice Hamiltonian for the"34-50"chiral gauge theory. We further show that $N$ copies of the modified Villain theory realize the $O(N,N;\mathbb{Z})$ T-duality transformations, which we then use to solve and analyze these lattice gauge theories.
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Chiral gauge theories revisitedM. Luscher · 2001 · arXiv: High Energy Physics - Theory · preprint, not peer reviewed · cited 73 times · Not summarized yet
Chiral gauge theories revisited surveys gauge anomalies, regularization, domain-wall fermions, Ginsparg-Wilson fermions, and gauge-invariant lattice constructions.
Abstract
Contents: 1. Introduction, 2. Chiral gauge theories & the gauge anomaly, 3. The regularization problem, 4. Weyl fermions from 4+1 dimensions, 5. The Ginsparg-Wilson relation, 6. Gauge-invariant lattice regularization of anomaly-free theories.
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Simulating lattice gauge theories within quantum technologiesM. Bañuls, R. Blatt, J. Catani et al. · 2019 · European Physical Journal D : Atomic, Molecular and Optical Physics · cited 660 times · Not summarized yet
Simulating lattice gauge theories within quantum technologies reviews quantum simulation motivations and applications of lattice gauge theories.
Abstract
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recen…
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Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson FermionsTanmoy Bhattacharya, M. Martin, E. Poppitz · 2006 · Physical Review D · cited 27 times · Not summarized yet
Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions proposes a two-dimensional construction using a warped three-dimensional theory.
Abstract
We propose a construction of a 2-dimensional lattice chiral gauge theory. The construction may be viewed as a particular limit of an infinite warped 3-dimensional theory. We also present a 'single-site' construction using Ginsparg-Wilson fermions which may avoid, in both 2 and 4 dimensions, the problems of waveguide-Yukawa models.
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Variational quantum simulation of U(1) lattice gauge theories with qudit systemsP. Popov, Michael Meth, Maciej Lewenstein et al. · 2023 · Physical Review Research · cited 45 times · Not summarized yet
Variational quantum simulation of U(1) lattice gauge theories with qudit systems maps Abelian gauge theories to locally interacting qudits and proposes a variational simulation scheme.
Abstract
Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map D-dimensional U(1) Abelian lattice gauge theories onto qudit systems with local interactions for arbitrary D. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in […
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