Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S

Author:

Bhardwaj Lakshya1,Giacomelli Simone123,Hübner Max14,Schäfer-Nameki Sakura1

Affiliation:

1. University of Oxford

2. INFN Sezione di Milano Bicocca

3. University of Milano-Bicocca

4. University of Pennsylvania

Abstract

A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theories that are boundary conditions of 7d7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d6d\mathcal{N}=(2,0)𝒩=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d4d\mathcal{N}=2𝒩=2 Class S theories. The defect group associated to such an irregular puncture provides extra “trapped” contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.

Funder

European Research Council

Horizon 2020

Instituto Nazionale di Fisica Nucleare

Simons Foundation

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

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