Relative Defects in Relative Theories: Trapped HigherForm Symmetries and Irregular Punctures in Class S
Abstract
A relative theory is a boundary condition of a higherdimensional topological quantum field theory (TQFT), and carries a nontrivial defect group formed by mutually nonlocal defects living in the relative theory. Prime examples are 6d N=(2,0) theories that are boundary conditions of 7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimensiontwo defects in 6d N=(2,0) theories, and find that the line defects living inside these codimensiontwo defects are mutually nonlocal and hence also form a defect group. Thus, codimensiontwo defects in a 6d N=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d bulk TQFT. A codimensiontwo defect carrying a nontrivial defect group acts as an irregular puncture when used in the construction of 4d N=2 Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and nonconformal 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 CalabiYau threefolds, and the other provided by ALE fibrations with monodromies.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2201.00018
 Bibcode:
 2022arXiv220100018B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 125 pages