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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T\overline{T }\)</EquationSource> </InlineEquation>-deformation, the root <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T\overline{T }\)</EquationSource> </InlineEquation>-deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.</p>

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

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  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Osamu Fukushima,
  • Takaki Matsumoto,
  • Kentaroh Yoshida

摘要

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 \(T\overline{T }\) -deformation, the root \(T\overline{T }\) -deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.