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Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories

Benini, Marco; Schenkel, Alexander; Vicedo, Benoît

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Authors

Marco Benini

Benoît Vicedo



Abstract

This paper provides a detailed study of 4-dimensional Chern-Simons theory on R2× CP1 for an arbitrary meromorphic 1-form ω on CP1. Using techniques from homotopy theory, the behaviour under finite gauge transformations of a suitably regularised version of the action proposed by Costello and Yamazaki is investigated. Its gauge invariance is related to boundary conditions on the surface defects located at the poles of ω that are determined by isotropic Lie subalgebras of a certain defect Lie algebra. The groupoid of fields satisfying such a boundary condition is proved to be equivalent to a groupoid that implements the boundary condition through a homotopy pullback, leading to the appearance of edge modes. The latter perspective is used to clarify how integrable field theories arise from 4-dimensional Chern-Simons theory.

Citation

Benini, M., Schenkel, A., & Vicedo, B. (2022). Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories. Communications in Mathematical Physics, 389, 1417-1443. https://doi.org/10.1007/s00220-021-04304-7

Journal Article Type Article
Acceptance Date Dec 25, 2021
Online Publication Date Jan 24, 2022
Publication Date Jan 1, 2022
Deposit Date Jan 20, 2022
Publicly Available Date Mar 28, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Science and Business Media LLC
Peer Reviewed Peer Reviewed
Volume 389
Pages 1417-1443
DOI https://doi.org/10.1007/s00220-021-04304-7
Keywords Mathematical Physics; Statistical and Nonlinear Physics
Public URL https://nottingham-repository.worktribe.com/output/7280308
Publisher URL https://link.springer.com/article/10.1007%2Fs00220-021-04304-7

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