2025/10/26 by Nissim, Ron
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2510.22788
We establish a mass gap, prove the existence of a unique infinite volume limit, and give a new proof of the large N limit for U(N) lattice Yang-Mills theory in the 't Hooft regime. These results were previously obtained for SU(N) and SO(N) lattice Yang-Mills theories as applications of the mixing of the associated Langevin dynamics, which is verified via the Bakry-Émery criterion [SZZ23]. For U(N), however, this approach fails because its Ricci curvature is not uniformly positive, and as a result the Bakry-Émery condition cannot be easily verified. To overcome this obstacle, we recast the U(N) theory as a random-environment SU(N) model, where the randomness arises from a U(1) field, and combine cluster-expansion and Langevin-dynamics techniques to analyze the resulting U(1)\timesSU(N) model.