<p>We construct generalized symmetries in two-dimensional symmetric product orbifold CFTs Sym<sup><i>N</i></sup>(<InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">T</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{T} \)</EquationSource> </InlineEquation>), for a generic seed CFT <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">T</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{T} \)</EquationSource> </InlineEquation>. These symmetries are more general than the universal and maximally symmetric ones previously constructed. We show that, up to one fine-tuned example when the number of copies <i>N</i> equals four, the only symmetries that can be preserved under twisted sector marginal deformations are invertible and maximally symmetric. The results are obtained in two ways. First, using the mathematical machinery of <i>G</i>-equivariantization of fusion categories, and second, via the projector construction of topological defect lines. As an application, we classify all preserved symmetries in symmetric product orbifold CFTs with the seed CFT given by any <i>A</i>-series <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mfenced close=")" open="(" separators=","> <mn>2</mn> <mn>2</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=\left(2,2\right) \)</EquationSource> </InlineEquation> minimal model. We comment on the implications of our results for holography.</p>

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Generalized symmetries and deformations of symmetric product orbifolds

  • Nathan Benjamin,
  • Suzanne Bintanja,
  • Yu-Jui Chen,
  • Michael Gutperle,
  • Conghuan Luo,
  • Dikshant Rathore

摘要

We construct generalized symmetries in two-dimensional symmetric product orbifold CFTs SymN( T \( \mathcal{T} \) ), for a generic seed CFT T \( \mathcal{T} \) . These symmetries are more general than the universal and maximally symmetric ones previously constructed. We show that, up to one fine-tuned example when the number of copies N equals four, the only symmetries that can be preserved under twisted sector marginal deformations are invertible and maximally symmetric. The results are obtained in two ways. First, using the mathematical machinery of G-equivariantization of fusion categories, and second, via the projector construction of topological defect lines. As an application, we classify all preserved symmetries in symmetric product orbifold CFTs with the seed CFT given by any A-series N = 2 2 \( \mathcal{N}=\left(2,2\right) \) minimal model. We comment on the implications of our results for holography.