On the Leading Order Term of the Lattice Yang-Mills Free Energy

2025/11/10 by Brennecke, Christian
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions

paper · doi:10.48550/arxiv.2511.07297

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

In \citeCha1, the leading order term of the free energy of U(N) lattice Yang-Mills theory in Λ_n=\0,…,n\^d⊂ ℤ^d was determined, for every N≥ 1 and d≥ 2. The formula is explicit apart from a contribution K_d which corresponds to the limiting free energy of lattice Maxwell theory with boundary conditions induced by the axial gauge. By suitably adjusting the boundary conditions, we provide an equivalent characterization of K_d that admits its explicit computation.

Citations

• Correlation decay for U(1) lattice Higgs theory: the case of small mass
• Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs
• Langevin dynamics of lattice Yang-Mills-Higgs and applications
• A scaling limit of SU(2) lattice Yang-Mills-Higgs theory
• Invariant measure and universality of the 2D Yang-Mills Langevin dynamic
• Correlation decay for finite lattice gauge theories at weak coupling
• A new derivation of the finite N master loop equation for lattice Yang-Mills
• The Yang-Mills heat flow with random distributional initial data
• Yang-Mills for probabilists
• The leading term of the Yang-Mills free energy
• Rigorous solution of strongly coupled SO(N) lattice gauge theory in the large N limit

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