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arXiv · 2509.22080

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

Osamu Fukushima·Takaki Matsumoto·Kentaroh Yoshida
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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 $T\bar{T}$-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.

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Osamu Fukushima, Takaki Matsumoto, Kentaroh Yoshida. 2025-09-26. The Courant-Hilbert construction in 4D Chern-Simons theory. https://doi.org/10.1007/jhep01(2026)122

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