Year: 2025
Type: article
Abstract: A bstract Since the inception of lattice QCD, a natural definition for the Yang-Mills instanton on lattice has been long sought for. In a recent work [1], one of authors showed the natural solution has to be organized in terms of bundle gerbes in higher homotopy theory / higher category theory, and introduced the principles for such a categorical construction. To pave the way towards actual numerical implementation in the near future, nonetheless, an explicit construction is necessary. In this paper we provide such an explicit construction for SU(2) gauge theory, with technical aspects inspired by Lüscher’s 1982 geometrical construction [2]. We will see how the latter is in a suitable sense a saddle point approximation to the full categorical construction. The generalization to SU( N ) will be discussed. The construction also allows for a natural definition of lattice Chern-Simons-Yang-Mills theory in three spacetime dimensions.
Source: Journal of High Energy Physics
Authors: Peng Zhang, Jing-Yuan Chen
Institution: Tsinghua University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G2353261696, G3746203731
OpenAlex ID: W4411195175