Generalized Instanton Symmetry Induced by Monopoles

TL;DR

This paper introduces a generalized instanton symmetry in 5d nonabelian gauge theories that measures monopole string charges, originating from 6d superconformal theories, and extends to a broad class of homotopy invariants.

Contribution

It proposes a new class of topological symmetries in 5d gauge theories derived from 6d theories, generalizing instanton symmetry to measure monopole charges.

Findings

Identifies a generalized instanton symmetry in 5d theories.

Shows the symmetry's origin from 6d superconformal field theory.

Proposes new homotopy invariants from boundary non-invertible symmetry defects.

Abstract

We point out that there exists a generalization of instanton symmmetry in the Coulomb phase of 5d nonabelian gauge theories which is capable of measuring a wider class of topological charges of monopole strings. The symmetry is invertible on compact spacetimes, but non-invertible on spacetimes with boundary. In the case of maximal supersymmetry, we show that this symmetry has a natural origin coming from the 6d $\mathcal N=(2,0)$ superconformal field theory under dimensional reduction. By generalizing this construction to any ADE gauge group, this allows us to propose a broad new class of homotopy invariants provided by the boundary non-invertible symmetry defects.