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

Autor: Marco Benini, Alexander Schenkel, Benoît Vicedo
Rok vydání: 2022
Předmět:
Zdroj: Communications in Mathematical Physics. 389:1417-1443
ISSN: 1432-0916
0010-3616
DOI: 10.1007/s00220-021-04304-7
Popis: This paper provides a detailed study of $4$-dimensional Chern-Simons theory on $\mathbb{R}^2 \times \mathbb{C}P^1$ for an arbitrary meromorphic $1$-form $\omega$ on $\mathbb{C}P^1$. 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 $\omega$ 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.
Comment: 27 pages; v2: Final version accepted for publication in Communications in Mathematical Physics
Databáze: OpenAIRE
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