Topology in 2D non-Abelian Lattice Gauge Theories

2024/11/18 by Stephan Dürr, Durr, Stephan, Philip Rouenhoff +1
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computational Geometry and Mesh Generation #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2411.11593

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In two dimensions, U(N_c) gauge theories exhibit a non-trivial topological structure, while SU(N_c) theories are topologically trivial. Hence, for G = U(N_c) the phase space is divided into topological sectors, characterized by a topological index (a.k.a. ``topological charge''). These sectors are separated by action barriers, which diverge if the lattice spacing is taken small, resulting in an algorithmic problem known as ``topological freezing''. We study these theories in various box sizes and at various couplings. With the help of gradient flow we derive instanton-like solutions for 2D U(N_c) theory with a specific focus on the case of N_c = 2.

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