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<p>The four-dimensional Chern-Simons (CS) theory provides a systematic procedure for realizing two-dimensional integrable field theories. It is therefore a natural question to ask whether integrable deformations of the theories can be realized in the four-dimensional CS theory. In this work, we study <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(T\overline{T}\)</EquationSource> </InlineEquation> and root-<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(T\overline{T}\)</EquationSource> </InlineEquation> deformations of two-dimensional integrable field theories, formulated in terms of dynamical coordinate transformations, within the framework of four-dimensional CS theory coupled to disorder defects. We illustrate our procedure in detail for the degenerate <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal{E}\)</EquationSource> </InlineEquation>-model, a specific construction that captures and unifies a broad range of integrable systems, including the principal chiral model.</p>

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\(T\overline{T}\) and root-\(T\overline{T}\) deformations in four-dimensional Chern-Simons theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月14日

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  • Jun-ichi Sakamoto,
  • Roberto Tateo,
  • Masahito Yamazaki

摘要

The four-dimensional Chern-Simons (CS) theory provides a systematic procedure for realizing two-dimensional integrable field theories. It is therefore a natural question to ask whether integrable deformations of the theories can be realized in the four-dimensional CS theory. In this work, we study \(T\overline{T}\) and root- \(T\overline{T}\) deformations of two-dimensional integrable field theories, formulated in terms of dynamical coordinate transformations, within the framework of four-dimensional CS theory coupled to disorder defects. We illustrate our procedure in detail for the degenerate \(\mathcal{E}\) -model, a specific construction that captures and unifies a broad range of integrable systems, including the principal chiral model.