Metraipolis › archive › dc_7b024bb6393b

Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting — arXiv:2610.09147

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.09147
License (as archived): CC0-1.0
Archived: 2026-10-08T12:36:46.108Z
SHA-256 of the archived text: b3d5a89e38cefde6388c71f90678ecd689a8e3ea6f22b9bbe8d6ae9ef927367d
Stable URL of this page: https://metraipolis.com/documento/dc_7b024bb6393b

How to cite

Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting — arXiv:2610.09147 — arXiv (en), https://arxiv.org/abs/2610.09147 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7b024bb6393b (Metraipolis archive dc_7b024bb6393b, sha256 b3d5a89e38cefde6388c71f90678ecd689a8e3ea6f22b9bbe8d6ae9ef927367d)

BibTeX

@misc{dc7b024bb6393b,
  title = {Sampling SU(N) gauge theory on a 2D lattice from independent plaquettes via holonomies and corner reweighting — arXiv:2610.09147},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.09147},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7b024bb6393b; sha256 b3d5a89e38cefde6388c71f90678ecd689a8e3ea6f22b9bbe8d6ae9ef927367d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.09147. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\mathrm{SU}(N)$ 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 $X,Y\in\mathrm{SU}(N)$ given the group commutator $Z=XYX^\dagger Y^\dagger$, where $Z\in\mathrm{SU}(N)$ 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 $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$. A normalizing flow models the single-plaquette distribution for $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$; for the group-commutator problem we use a closed-form sampler for $\mathrm{SU}(2)$ and a trained normalizing flow for $\mathrm{SU}(3)$. In our tests on $2\times2$ and $32\times32$ 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.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: High Energy Physics - Lattice (hep-lat) ; Machine Learning (cs.LG); High Energy Physics - Theory (hep-th).
Pagina del lavoro: https://arxiv.org/abs/2610.09147 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T12:14:15.379Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).