The Courant-Hilbert construction in 4D Chern-Simons theory

We consider the Courant-Hilbert (CH) construction of integrable deformations of a two-dimensional principal chiral model (2D PCM) in the context of the four-dimensional Chern-Simons (4D CS) theory. According to this construction, an integrable deformation of 2D PCM is characterized by a boundary function. As a result, the master formula obtained from the 4D CS theory should be corrected by the trace of the energy-momentum tensor so as to support the CH construction. We present some examples of deformation including the $T\bar{T}$-deformation, the root $T\bar{T}$-deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.

💡 Research Summary

The paper investigates integrable deformations of the two‑dimensional principal chiral model (PCM) by embedding the Courant‑Hilbert (CH) construction into the four‑dimensional Chern‑Simons (4D CS) framework. Starting from the 4D CS action (S