The Courant-Hilbert construction in 4D Chern-Simons theory
Abstract
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 -deformation, the root -deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.
Cite
@article{arxiv.2509.22080,
title = {The Courant-Hilbert construction in 4D Chern-Simons theory},
author = {Osamu Fukushima and Takaki Matsumoto and Kentaroh Yoshida},
journal= {arXiv preprint arXiv:2509.22080},
year = {2026}
}
Comments
25 pages; v2: typos corrected, references and some comments added; v3: clarifications and an appendix added, published version in JHEP