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<p>We investigate the interplay between (<i>−</i>1)-form symmetries and their quantum-dual (<i>d</i> − 1)-form counterparts within the framework of Symmetry Topological Field Theories (SymTFTs). In this framework the phenomenon of decomposition — a <i>d</i>-dimensional quantum field theory with (<i>d</i> − 1)-form symmetry being the disjoint union of other theories (or “universes”) — arises naturally from manipulations of topological boundary conditions of the SymTFT. We corroborate our findings with various examples, including a generalization of “instanton-restricted” 4d Yang-Mills theories with no sum over instanton sectors. Furthermore, we construct a 3d SymTFT with a non-invertible (<i>−</i>1)-form symmetry. The absolute 2d quantum field theory includes a 0-form global symmetry that depends on a parameter whose value gets shifted by the action of the (<i>−</i>1)-form symmetry, and we show that the non-invertibility of the latter is needed to encode this modification of the 0-form symmetry.</p>

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Decomposition and (non-invertible) (−1)-form symmetries from the symmetry topological field theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月16日

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  • Ling Lin,
  • Daniel Robbins,
  • Subham Roy

摘要

We investigate the interplay between (−1)-form symmetries and their quantum-dual (d − 1)-form counterparts within the framework of Symmetry Topological Field Theories (SymTFTs). In this framework the phenomenon of decomposition — a d-dimensional quantum field theory with (d − 1)-form symmetry being the disjoint union of other theories (or “universes”) — arises naturally from manipulations of topological boundary conditions of the SymTFT. We corroborate our findings with various examples, including a generalization of “instanton-restricted” 4d Yang-Mills theories with no sum over instanton sectors. Furthermore, we construct a 3d SymTFT with a non-invertible (−1)-form symmetry. The absolute 2d quantum field theory includes a 0-form global symmetry that depends on a parameter whose value gets shifted by the action of the (−1)-form symmetry, and we show that the non-invertibility of the latter is needed to encode this modification of the 0-form symmetry.