Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopical analysis of 4d Chern-Simons theory and integrable field
  theories   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.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex