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A formula for Wilson loop expectations in 2d Yang–Mills theory
Multi angle
Authors : Lévy, Thierry (Author of the conference)
CIRM (Publisher )
05E10 - Combinatorial aspects of representation theory
60G65 - Nonlinear processes (e.g., G -Brownian motion, G -Lévy processes)
81T13 - Yang-Mills and other gauge theories
CIRM (Publisher )
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Abstract :
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.
Keywords : Yang–Mills measure; Wilson loop expectations; Schur–Weyl duality; random partitions
MSC Codes : Keywords : Yang–Mills measure; Wilson loop expectations; Schur–Weyl duality; random partitions
05E10 - Combinatorial aspects of representation theory
60G65 - Nonlinear processes (e.g., G -Brownian motion, G -Lévy processes)
81T13 - Yang-Mills and other gauge theories
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/11/2024 Conference Date : 08/10/2024 Subseries : Research talks arXiv category : Mathematical Physics ; Probability Mathematical Area(s) : Combinatorics ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:49:04 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-10-07_Levy.mp4 
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Information on the Event
Event Title : Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoiresEvent Organizers : Bordenave, Charles ; Capitaine, Mireille ; Chhaibi, Reda ; Collins, Benoît ; Defosseux, Manon ; Demni, Nizar Dates : 07/10/2024 - 11/10/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3052.html
Citation Data
DOI : 10.24350/CIRM.V.20255303Cite this video as: Lévy, Thierry (2024). A formula for Wilson loop expectations in 2d Yang–Mills theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20255303 URI : http://dx.doi.org/10.24350/CIRM.V.20255303 |
See Also
- [Multi angle] The Fuglede-Kadison determinant of matrix-valued semicircular elements and the noncommutative Edmonds' problem / Author of the conference Mai, Tobias.
- [Multi angle] Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations / Author of the conference de la Salle, Mikael.
- [Multi angle] Large deviations for macroscopic observables of heavy-tailed matrices / Author of the conference Guionnet, Alice.
- [Multi angle] Linear eigenvalue statistics of polynomials in a Wigner matrix and a diagonal deterministic matrix / Author of the conference Dallaporta, Sandrine.
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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