A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.
Chern-Simons Theory and the $R$-Matrix
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abstract
It has been a long-standing problem how to relate Chern-Simons theory to the quantum groups. In this paper we recover the classical $r$-matrix directly from a 3-dimensional Chern-Simons theory with boundary conditions, thus creating a direct link to the quantum groups. It is known that the Jones polynomials can be constructed using an $R$-matrix. We show how these constructions can be seen to arise directly from 3-dimensional Chern-Simons theory.
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Gauge Theory And Integrability, III
A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.