2024/05/13 by Schenkel, Alexander, Vicedo, Benoit · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2405.08083
The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field theories. The purpose of this paper is to extend this framework to the setting of 3-dimensional integrable field theories by considering a 5-dimensional semi-holomorphic higher Chern-Simons theory for a higher connection (A,B) on ℝ3 × ℂP1. The input data for this theory are the choice of a meromorphic 1-form ω on ℂP1 and a strict Lie 2-group with cyclic structure on its underlying Lie 2-algebra. Integrable field theories on ℝ3 are constructed by imposing suitable boundary conditions on the connection (A,B) at the 3-dimensional defects located at the poles of ω and choosing certain admissible meromorphic solutions of the bulk equations of motion. The latter provides a natural notion of higher Lax connection for 3-dimensional integrable field theories, including a 2-form component B which can be integrated over Cauchy surfaces to produce conserved charges. As a first application of this approach, we show how to construct a generalization of Ward's (2+1)-dimensional integrable chiral model from a suitable choice of data in the 5-dimensional theory.