A formula for Wilson loop expectations in 2d Yang–Mills theory | Vidéo | Carmin.tv

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

By Thierry Lévy

Appears in collection : Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires

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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