The Courant-Hilbert construction in 4D Chern-Simons theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912886370074624 |
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| author | Fukushima, Osamu Matsumoto, Takaki Yoshida, Kentaroh |
| author_facet | Fukushima, Osamu Matsumoto, Takaki Yoshida, Kentaroh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Courant-Hilbert construction in 4D Chern-Simons theory Fukushima, Osamu Matsumoto, Takaki Yoshida, Kentaroh High Energy Physics - 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. |
| title | The Courant-Hilbert construction in 4D Chern-Simons theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.22080 |