Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires

Collection Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires

Organizer(s) Bordenave, Charles ; Capitaine, Mireille ; Chhaibi, Reda ; Collins, Benoît ; Defosseux, Manon ; Demni, Nizar

Date(s) 07/10/2024 - 11/10/2024

linked URL https://conferences.cirm-math.fr/3052.html

00:00:00 / 00:00:00

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A formula for Wilson loop expectations in 2d Yang–Mills theory

By Thierry Lévy

Wilson loops are the basic observables of Yang—Mills theory, and their expectation is rigorously defined on the Euclidean plane and on a compact Riemannian surface. Focusing on the case where the structure group is the unitary group, I will present a formula that computes any Wilson loop expectation in almost purely combinatorial terms, thanks to the dictionary between unitary and symmetric quantities provided by the Schur-Weyl duality.

Information about the video

Date of recording 08/10/2024
Date of publication 04/11/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20255303
Cite this video Lévy, Thierry (08/10/2024). A formula for Wilson loop expectations in 2d Yang–Mills theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20255303
URL https://dx.doi.org/10.24350/CIRM.V.20255303

Domain(s)

Bibliography

LÉVY, Thierry. Schur–Weyl duality and the heat kernel measure on the unitary group. Advances in Mathematics, 2008, vol. 218, no 2, p. 537-575. - https://doi.org/10.1016/j.aim.2008.01.006
LÉVY, Thierry. Two-dimensional quantum Yang–Mills theory and the Makeenko–Migdal equations. In : Frontiers in Analysis and Probability: In the Spirit of the Strasbourg-Zürich Meetings. Springer International Publishing, 2020. p. 275-325. - http://dx.doi.org/10.1007/978-3-030-56409-4_7
OKOUNKOV, Andrei et VERSHIK, Anatoly. A new approach to representation theory of symmetric groups. Selecta Mathematica, 1996, vol. 2, no 4, p. 581. - https://www.uwaterloo.ca/scholar/sites/ca.scholar/files/b2webste/files/vershik-okounkov.pdf
WITTEN, Edward. On quantum gauge theories in two dimensions. Communications in Mathematical Physics, 1991, vol. 141, no 1, p. 153-209. - http://dx.doi.org/10.1007/BF02100009

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