The Courant-Hilbert construction in 4D Chern-Simons theory (Part 1)

Abstract: Recently, the method developed by Courant and Hilbert (CH) has been shown to be able to generally describe various integrable deformations of the 2D principal chiral model, including the TTbar deformation and the root TTbar deformation. We show how this CH method can be described in 4D Chern-Simons (4D CS) theory. In particular, for deformations with a dimensionful parameter such as the TTbar deformation, a correction term, the trace of the energy-momentum tensor, must be added to the original 4D CS theory. This correction term is consistent with the result shown by Sakamoto-Tateo-Yamazaki (2509.12303 [hep-th]) for the TTbar deformation and is generalized by the CH method.

This talk is based on the collaboration 2509.22080 [hep-th] with Osamu Fukushima (RIKEN iTHEMS) and Takaki Matsumoto (Seikei University).

In the first part, we introduce some basics of the TTbar deformation and the root TTbar deformation, then we describe the CH construction of integrable deformations of the 2D principal chiral model.

In the second part, we show how this CH method can be described in 4D CS theory.

high energy physicsmathematical physicsnonlinear sciences

Audience: researchers in the topic

Nagoya IAR workshop on Unification of Integrable Systems