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.

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

Benini M.;
2022

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/1069768
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