English

Worldvolume Hybrid Monte Carlo algorithm for group manifolds

High Energy Physics - Lattice 2026-03-31 v3 High Energy Physics - Theory

Abstract

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches while maintaining low computational costs. In this paper, as a general framework for applying WV-HMC to lattice gauge theories, we extend the algorithm to systems defined on compact group manifolds. The key is to introduce a symplectic structure on the tangent bundle of the worldvolume and formulate molecular dynamics upon it. The validity of the proposed algorithm is demonstrated using the one-site model with a purely imaginary coupling constant.

Keywords

Cite

@article{arxiv.2506.12002,
  title  = {Worldvolume Hybrid Monte Carlo algorithm for group manifolds},
  author = {Masafumi Fukuma},
  journal= {arXiv preprint arXiv:2506.12002},
  year   = {2026}
}

Comments

65 pages, 11 figures; v2: typos corrected, figures updated; v3: typos corrected, proof of symplecticity elaborated

R2 v1 2026-07-01T03:16:28.852Z