Quantum Yang-Mills Theory in Two Dimensions

Research video based on the papers arxiv:1508.06305, arxiv:1601.04726, arxiv:1607.07463.

Part One (general introduction):
0:26 - two paradigms for understanding quantum Yang-Mills theory
0:38 - perturbative formulation (Feynman diagrams)
1:20 - lattice formulation
2:38 - lattice vs. perturbative formulation
2:51 - the basic question
3:40 - why this question is fundamental
4:15 - Millennium Problem
4:43 - Migdal-Witten lattice formulation (heat kernels)
4:56 - definition of Wilson loop
5:37 - the precise question in 2D
6:15 - sociological remarks

Part Two (technical results):
6:55 - intro + visual overview of results
8:07 - Coulomb gauge (metric-independence using Batalin-Vilkovisky quantization)
10:20 - holomorphic gauge = Coulomb gauge (uses complexification)
12:13 - holomorphic gauge yields Gaussian matrix integrals (uses iterated integrals)
13:24 - Wu-Mandelstam-Liebrandt regularization
13:35 - axial gauge
13:54 - stochastic axial-gauge
14:56 - inequivalence of stochastic axial-gauge and holomorphic gauge
15:50 - algebraic stochastic calculus
16:41 - future directions

Notes:

4:44 - Our attribution Migdal-Witten is one suggested from the monograph arxiv:0101239, owing to Migdal's original formulation in 1976 and Witten's seminal work on 2D Yang-Mills in the early 90s. We acknowledge that much work had been done on 2D Yang-Mills in between those years.

16:55 - It follows from holomorphic gauge = Coulomb gauge and arxiv:0906.1572 that one can get asymptotics to all orders for simple closed curves in holomorphic gauge. Thus, I am now working to extend such results to self-intersecting curves.