Vladimir Kazakov教授学术报告
Title: Bootstrap for matrix models and lattice Yang-Mills theory at large N
Speaker: Vladimir Kazakov
Affiliation: Ecole Normale Supérieure Paris, France（巴黎高等师范学院）
Université Paris-VI (Université Pierre et Marie Curie) （巴黎第六大学）
Time: 16:00-17:00, Tuesday, 26th April, 2022 (UTC+8, Beijing Time)
Venue：Zoom Meeting
Inviter: Yunfeng JIANG (江云峰)
Vladimir Kazakov-Bootstrap for matrix models and lattice Yang-Mills theory at large N_20220426.pdf
Abstract
I will speak about my recent work with Zechuan Zheng where we study the SU(Nc) lattice Yang-Mills theory in the ’t Hooft limit N → infinity, at dimensions D=2,3,4, via the numerical boot strap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on maximal length of loops, and the positivity conditions on certain correlation matrices. Our algorithm is inspired by the pioneering paper of P.Anderson and M.Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in the line with our previous work on matrix bootstrap. We thus obtain the rigorous upper and lower bounds on plaquette average at various couplings and dimensions. The results are quickly improving with the increase of cutoff L. For D=4 and L=16, the lower bound data appear to be close to the Monte Carlo data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. We attempt to extract the information about the gluon condensate from this data. Our results suggest that this bootstrap approach can provide a tangible alternative to, so far uncontested, Monte Carlo approach. I will also mention our results on the bootstrap approach for an unsolvable two-matrix model in the large N limit. Matrix bootstrap appears to be superior in efficient over Monte Carlo.
About the Speaker
Prof. Vladimir Kazakov is a Russian-French theoretical physicist, working currently as a full professor at the Ecole Normale Supérieure, Paris and the Université Paris-VI (Université Pierre et Marie Curie). He is a world’s leading expert in matrix models, 2d gravity and integrability.
He was awarded the Landau-Weizmann Award of the Weizmann Institute of Science (Israel), Senior Member of Institut Universitaire de France (from 2003), Servant Award of French Academy of Sciences (2007), Gay-Lussac Humboldt Award (Germany, 2007).
His personal page: http://www.phys.ens.fr/~kazakov/
The seminar will be broadcasted online by Zoom.
Interested people are free to join, without registration in advance.
The Zoom info is
URL: https://us02web.zoom.us/j/3854420225?pwd=SXY4eWJKOTBFZWJDaE16aXpTamY1QT09
Meeting ID: 385 442 0225
Passcode: yauc