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<p>We apply the cobordism hypothesis with singularities to the case of affine Rozansky–Witten models, providing a construction of extended TQFTs that includes all line and surface defects. On a technical level, this amounts to proving that the associated homotopy 2-category is pivotal, and to systematically employing its 3-dimensional graphical calculus. This in particular allows us to explicitly calculate state spaces for surfaces with arbitrary defect networks. As specific examples we discuss symmetry defects which can be used to model non-trivial background gauge fields, as well as boundary conditions.</p>

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Truncated Affine Rozansky–Witten Models as Extended Defect TQFTs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月28日

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  • Ilka Brunner,
  • Nils Carqueville,
  • Pantelis Fragkos,
  • Daniel Roggenkamp

摘要

We apply the cobordism hypothesis with singularities to the case of affine Rozansky–Witten models, providing a construction of extended TQFTs that includes all line and surface defects. On a technical level, this amounts to proving that the associated homotopy 2-category is pivotal, and to systematically employing its 3-dimensional graphical calculus. This in particular allows us to explicitly calculate state spaces for surfaces with arbitrary defect networks. As specific examples we discuss symmetry defects which can be used to model non-trivial background gauge fields, as well as boundary conditions.