Generalized Instanton Symmetry Induced by Monopoles

TL;DR

This work reveals a generalized instanton symmetry in the Coulomb phase of 5d nonabelian gauge theories that can detect refined monopole-string topological charges, especially when monopole strings wrap a spatial circle. The symmetry is invertible on compact manifolds but non-invertible on spaces with boundary, realized by boundary TQFTs derived from a Pontryagin-square-based bulk theory and a minimal abelian TQFT, with the current $J_I=rac{1}{8\pi^2}\mathrm{Tr}(F\wedge F)$ playing a central role. The origin is established via circle reduction of the 6d $\mathcal N=(2,0)$ theory and its SymTFT description, which naturally yields the generalized defects and their boundary realizations; the construction extends to ADE gauge groups through a generalized bulk-boundary framework that could encode homotopy invariants of monopole winding classes. Overall, the paper proposes a broad class of boundary non-invertible symmetry defects that refine instanton symmetry and suggest new topological invariants tied to monopole strings in 5d gauge theories with potential links to UV completions and tensor-branch dynamics.

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.