Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S

Understand

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 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 codimension-two defects in 6d 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 6d N=(2,0) theory are relative defects living inside a relative theory.