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1-form Symmetries of 4d N=2 Class S Theories

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arxiv 2102.01693 v2 pith:36IACADO submitted 2021-02-02 hep-th

Lakshya Bhardwaj , Max Hubner , Sakura Schafer-Nameki This is my paper · ORCID
classification hep-th
keywords formgroupoperatorstheoryclassmutuallysurfacesymmetry
verification ladder T0 review T1 audit T2 compute T3 formal
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We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

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Cited by 3 Pith papers

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  1. Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

    hep-th 2024-11 conditional novelty 8.0 of 10

    For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.

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    The Higgs branches of 5d conformal matter atoms and molecules are computed via magnetic quivers and class-S circle reductions, with matching dimensions across the two methods.

  3. Symmetry, Symmetry Topological Field Theory and von Neumann Algebra

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    The symmetric-sector von Neumann algebra of a QFT violates additivity or Haag duality exactly when the Lagrangian algebra of its SymTFT contains operators beyond the identity, with a sharper criterion distinguishing t...

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