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

Benini, Marco; Schenkel, Alexander; Vicedo, Benoît

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 4, 2022
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• 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