On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories

Understand

Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects.

• Symmetry groups are thus Brauer-Picard groups.
• We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories.
• The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group $A$, and with vanishing 3-cocycle, is generated by group automorphisms of $A$, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of $A$-bundles, and by partial e-m dualities.