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
Subject
General Physics and Astronomy
Cited by
27 articles.
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