A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.
Construction of Lax Connections by Exponentiation
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abstract
We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must satisfy for an entire one-parameter family of connections to be flat.
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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.