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

Abstract: In a recent paper, S. Chatterjee determined the leading order term of the free energy of U(N) lattice Yang-Mills theory in $\Lambda_n=\{0,\ldots,n\}^d\subset \bZ^d$, for every $N\geq 1$ and $d\geq 2$. 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. After a brief motivation, I recall some of the key steps to obtain the leading order term of the free energy and I explain an equivalent characterization of $K_d$ that admits its explicit computation, for every $d\geq 2$.

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields

Series comments: Paweł Duch (EPFL) will give a mini-course on "Singular Stochastic PDEs", in the period March 9-20, 2026.