A dynamical approach to lattice Yang-Mills

Lattice Yang-Mills is a model of a collection of matrices. We consider its Langevin dynamic (stochastic quantization) which is a system of SDEs. Using this SDE system, we give a simple derivation of the Makeenko-Migdal loop equations, prove uniqueness and ergodicity, log-Sobolev and Poincare inequalities, large N limits and exponential decay of correlations at strong coupling. These are based on joint works with Scott Smith, Rongchan Zhu and Xiangchan Zhu. The dynamics in continuum in 2D and 3D have been recently constructed by Chandra, Chevyrev, Hairer and the speaker, and part of the motivation of the talk is to see if certain properties of the YM model can be extracted from the dynamics with a simplification of a lattice cutoff.

• Speaker: Hao Shen (Wisconsin, Madison)
• Tuesday 07 June 2022, 14:00–15:00
• Venue: MR12, Centre for Mathematical Sciences.
• Series: Probability; organiser: Perla Sousi.