SymTFTs and duality defects from 6d SCFTs on 4-manifolds

In this work we study particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d (2, 0) SCFTs on 4-manifolds M4. The mapping class group of M4 and the automorphism group of the SymTFT switch between different absolute 2d theories or global variants. Using the combined symmetries, we realize the topological defects in these global variants. Our main example is DOUBLE-STRUCK CAPITAL P1 x DOUBLE-STRUCK CAPITAL P1. For N M5-branes the corresponding 2d theory inherits DOUBLE-STRUCK CAPITAL ZN 0-form symmetries from the SymTFT. We reproduce the orbifold groupoid for theories with DOUBLE-STRUCK CAPITAL ZN 0-form symmetries and realize the duality defects at fixed points of the coupling constant under elements of the mapping class group. We also study other Hirzebruch surfaces, del Pezzo surfaces, as well as the connected sum of DOUBLE-STRUCK CAPITAL P1 x DOUBLE-STRUCK CAPITAL P1. We find a rich network of global variants connected via automorphisms and realize more interesting topological defects. Finally, we derive the SymTFT on more general 4-manifolds and provide two examples.