English

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

High Energy Physics - Theory 2021-12-01 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2102.01693,
  title  = {1-form Symmetries of 4d N=2 Class S Theories},
  author = {Lakshya Bhardwaj and Max Hubner and Sakura Schafer-Nameki},
  journal= {arXiv preprint arXiv:2102.01693},
  year   = {2021}
}

Comments

62 pages, 43 TikZ figures; v2: Important typos corrected