Bootstrap for finite N lattice Yang-Mills theory

• Published in: The journal of high energy physics Vol. 2025; no. 3; pp. 99 - 40
• Main Authors: Kazakov, Vladimir, Zheng, Zechuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 13.03.2025; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Algorithms; Algorithms and Theoretical Developments; Classical and Quantum Gravitation; Convexity; Couplings; Elementary Particles; Field Theories in Higher Dimensions; Free energy; High energy physics; High Energy Physics - Lattice; High Energy Physics - Theory; Linearity; Nonperturbative Effects; Physics; Physics and Astronomy; Qualitative analysis; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Statistical methods; String Theory; Variables; Wilson, ’t Hooft and Polyakov loops; Yang-Mills theory; Algorithms and Theoretical Developments; Wilson, ’t Hooft and Polyakov loops; Field Theories in Higher Dimensions; Nonperturbative Effects; efficiency; SU; matrix model; bootstrap; Wilson loop; 4; free energy; Monte Carlo; string tension; lattice; Yang-Mills; loop equation; gauge field theory; dimension
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP03(2025)099

A bstract We introduce a comprehensive framework for analyzing finite N lattice Yang-Mills theory and finite N matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear and closed exclusively on single-trace Wilson loops. This inherent linearity significantly improves the efficiency of the bootstrap approach by leveraging the problem’s convexity, permitting the inclusion of Wilson loops up to length 24. The exact upper and lower margins for the free energy per plaquette, derived from our bootstrap method, demonstrate good agreement with Monte Carlo data, achieving precision within 0 . 1% for the physically relevant range of couplings in both three and four dimensions. Additionally, our bootstrap data provides estimates of the string tension, in qualitative agreement with existing Monte Carlo computations.