Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories
Abstract
Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.
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BibTeX
@misc{singha2026sectorresolved,
title = {{Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories}},
author = {Ankur Singha and Jacob Kauffmann and Karl Jansen and Jacob Finkenrath and Vipul Arora and Shinichi Nakajima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07781},
eprint = {2609.07781},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07781},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories
AU - Ankur Singha
AU - Jacob Kauffmann
AU - Karl Jansen
AU - Jacob Finkenrath
AU - Vipul Arora
AU - Shinichi Nakajima
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07781
UR - https://arxiv.org/abs/2609.07781
AB - Topological fluctuations are essential to nonperturbative gauge theories but become increasingly difficult to sample toward the continuum limit, where Markov chains can freeze in sectors of fixed topological charge. We introduce a generative sampler, a mixture of sector-resolved samplers (MSRS) that explicitly resolves these sectors and exploits a key advantage of generative models, the ability to directly evaluate the domain-restricted partition function and thereby determine the relative weights of disconnected sectors. We train a generative model in a reference topological sector combined with a bijective topological shift that deterministically maps its samples to other sectors. We demonstrate the method in two-dimensional compact U (1) lattice gauge theory, where it reproduces the topological-charge distribution and yields an unbiased susceptibility in a regime where hybrid Monte Carlo is frozen and overrelaxation gives inaccurate estimates. Our approach also outperforms existing flow-based samplers by orders of magnitude. These results demonstrate that explicit sector resolution provides a promising route to overcoming topological barriers in lattice gauge theory.
ER -