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<p>We introduce a formalism for constructing cohomological field theories (CohFTs), inspired by Witten’s paradigm of “symmetries, fields, and equations”. We apply this formalism to various first-order nonlinear PDEs and show that the resulting CohFTs agree with those previously proposed by physicists. In particular, applying it to the generalized Seiberg–Witten equations provides a unified perspective on the supersymmetric action functionals of the Donaldson–Witten, Seiberg–Witten, and Kapustin–Witten theories.</p>

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Cohomological Field Theories and First-Order Nonlinear PDEs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月6日

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  • Shuhan Jiang,
  • Jürgen Jost

摘要

We introduce a formalism for constructing cohomological field theories (CohFTs), inspired by Witten’s paradigm of “symmetries, fields, and equations”. We apply this formalism to various first-order nonlinear PDEs and show that the resulting CohFTs agree with those previously proposed by physicists. In particular, applying it to the generalized Seiberg–Witten equations provides a unified perspective on the supersymmetric action functionals of the Donaldson–Witten, Seiberg–Witten, and Kapustin–Witten theories.