Holography and discrete theta angles for disconnected gauge groups

TL;DR

This paper uses holography to derive the symmetry TFT for $ ext{SO}(2n)$ $ ext{N}=4$ SYM, revealing new terms and analyzing global forms, discrete theta angles, and S-duality predictions for disconnected gauge groups.

Contribution

It introduces a holographic derivation of the symmetry TFT for $ ext{SO}(2n)$ gauge theories, including previously unaccounted terms, and explores their boundary conditions and dualities.

Findings

Derived the symmetry TFT including new holographic terms.

Connected boundary conditions to global forms and discrete theta angles.

Predicted S-duality relations for theories with disconnected gauge groups.

Abstract

Starting from holography, we derive the symmetry TFT for $\mathcal{N}=4$ SYM with $\mathfrak{so}(2n)$ gauge algebra, including terms which were previously unaccounted for holographically, by considering the action of the symmetry TFT on manifolds with torsion cycles. We then study gapped boundary conditions of the symmetry TFT and show how they correspond to the global forms and discrete theta angles studied by Hsin and Lam, including their higher group and non-invertible symmetries and anomalies. In particular, we analyse the case of theories with disconnected gauge groups. Considering the action of S-duality on the boundary conditions then leads to predictions for S-duality between these theories.