HEP Lattice·hep-lat

Thu·Oct 8, 2026Thursday·October 8, 2026

7 papers—5 primary·2 cross-listed

01
A gauge-invariant measure for lattice chiral fermions
Nathaniel Craig
We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.
hep-lathep-phhep-th
02
Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting
Javad Komijani
In the Wilson formulation of lattice gauge theory, the fundamental degrees of freedom are group-valued link variables, while the action is a sum over the trace of the plaquettes, the smallest Wilson loops. For generative sampling methods such as normalizing flows, this poses a challenge: the distribution of an individual plaquette is easy to model, but mapping sampled plaquettes to the links is the obstruction. We explore a statistical way around this in two dimensions for the $SU (N)$ gauge theory with the Wilson plaquette action. The action can be written in terms of holonomy variables, which determine the links once a consistency condition at the four corners of an extended lattice is satisfied. Using a boundary condition that only affects the holonomies, we trade this consistency condition for a conditional sampling problem, which reduces to sampling $X, Y \in SU (N)$ given the group commutator $Z = X Y X^{†} Y^{†}$ , where $Z \in SU (N)$ depends on the four corners. Plaquettes are sampled independently, and the resulting configurations carry weights due to the additional conditional sampling. We obtain the density of $Z$ , which determines these weights, in closed form for $SU (2)$ and $SU (3)$ . A normalizing flow models the single-plaquette distribution for $SU (2)$ and $SU (3)$ ; for the group-commutator problem we use a closed-form sampler for $SU (2)$ and a trained normalizing flow for $SU (3)$ . In our tests on $2 \times 2$ and $32 \times 32$ lattices at two couplings each, per-plaquette acceptance rates exceed $99%$ and the effective sample size of the final weights is moderate, typically above one half.
hep-latcs.LGhep-th
03
Performance Portable $SU (N)$ Lattice Gauge Theory Simulation with Kokkos
Wei Sun
The increasing diversity of high performance computing systems makes separate, architecture specific implementations of lattice gauge theory algorithms costly to maintain. We present \texttt{kwqft}, a performance portable Kokkos implementation of Wilson pure gauge Monte Carlo simulation for $SU (N)$ Yang-Mills theory in an arbitrary number of space-time dimensions. The gauge group order $N$ and the dimension $D$ are compile time parameters. A single source targets the Serial, OpenMP, CUDA, HIP, and SYCL execution spaces, with MPI halo exchange overlapped with interior updates. The implementation reproduces the exact two-dimensional plaquette and published three and four dimensional values for gauge groups up to $SU (17)$ . On an NVIDIA A100 the Kokkos CUDA backend is competitive with a native CUDA code, SIMD acceleration improves the OpenMP path on Armv9 processors, and a large scale speedup is demonstrated for an $SU (4)$ lattice on the LineShine supercomputer, currently ranked first on the TOP500 list.
hep-latcs.DChep-phphysics.comp-ph
04
Bjorken sum rule down to the elastic region from the lattice
J. A. Crawford · A. Hannaford-Gunn · R. Horsley · P. E. L. Rakow · T. G. Schar · G. Schierholz · H. Stüben · R. D. Young · J. M. Zanotti
We present a lattice determination of the Bjorken sum rule via a Feynman-Hellmann calculation of the polarised forward Compton amplitude. We evaluate the lowest moment of the nucleon's polarised structure function, $g_{1}$ , which we calculate over the range $0.5 ≲ Q^{2} ≲ 8$ GeV $^{2}$ , covering both non-perturbative and perturbative regions. We compare our calculated moments with the Bjorken sum rule, and discuss implications for the calculation of higher-twist effects, as well as evaluations of $α_{s} (Q^{2})$ from hadronic quantities to complement phenomenological and other lattice methods.
hep-lathep-phnucl-th
05
Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter
Jishnu Goswami · Frithjof Karsch · Sabarnya Mitra
We present results from a detailed finite-size scaling analysis of the $3$ - $d$ , $Z (2)$ and $O (2)$ spin models in an external field $H$ . Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to $z_{L}^{2} = 1/ (H L^{3/ (1 + 1/ δ))})^{2}$ . This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing $H$ . In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3$ - $d$ , $O (2)$ and $Z (2)$ universality classes.
hep-latcond-mat.stat-mechhep-ph
06
Fractal phase structure of QCD under imaginary rotation
Rin Takada🇯🇵
We show that in hot QCD rotating at an imaginary angular velocity $Ω_{I}$ , the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $θ$ , with $Ω_{I} /2 π = p / q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T / q$ and imaginary quark chemical potential $θ^{'} = q θ + π (p + q + 1)$ ; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T > q T_{RW}$ , with $T_{RW}$ the RW endpoint temperature. The bulks at $Ω_{I} = 2 π /3$ and $4 π /3$ , for example, are both at temperature $T /3$ , yet only the former can break $C$ . The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $Ω_{I} /2 π$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.
↳ hep-phhep-th0 citations
07
Two-pion exchange potential in $D^{(*)} D^{(*)}$ system
Daiki Suenaga · Masayasu Harada
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 $D D^{*}$ 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 $^{2}$ LO) 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 $0.5 fm ≲ r$ is reproduced by adjusting the unknown $O (p^{2})$ couplings. In particular, it turns out that contributions from isospin-independent N $^{2}$ LO triangle diagrams play a central role in reproducing the lattice data of the form $V^{D D^{*}} \sim (e^{- m_{π} r} / r)^{2}$ in $1.0 fm ≲ r ≲ 2.0 fm$ . 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.
↳ hep-phhep-latnucl-th

Affiliations

first authorsco-authorsvia INSPIRE

A gauge-invariant measure for lattice chiral fermions

Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting

Performance Portable SU(N) Lattice Gauge Theory Simulation with Kokkos

Bjorken sum rule down to the elastic region from the lattice

Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter

Fractal phase structure of QCD under imaginary rotation

Two-pion exchange potential in D(∗)D(∗) system

Affiliations

Performance Portable $SU (N)$ Lattice Gauge Theory Simulation with Kokkos

Two-pion exchange potential in $D^{()} D^{()}$ system