Instanton Operators and the Higgs Branch at Infinite Coupling

TL;DR

This paper explores how instanton operators influence the Higgs branch structure of 5d supersymmetric gauge theories at infinite coupling, revealing quantum corrections and new relations in the chiral ring.

Contribution

It explicitly derives the chiral ring relations involving instanton operators at infinite coupling for various 5d gauge theories, highlighting quantum corrections and operator dressings.

Findings

Glueball superfield becomes non-nilpotent at infinite coupling

Classical chiral ring relations are quantum corrected by instanton bilinears

Explicit expressions for instanton operator dressings of arbitrary charge

Abstract

The richness of 5d $\mathcal{N}=1$ theories with a UV fixed point at infinite coupling is due to the existence of local disorder operators known as instanton operators. By considering the Higgs branch of $SU(2)$ gauge theories with $N_f \leq 7$ flavours at finite and infinite coupling, we write down the explicit chiral ring relations between instanton operators, the glueball superfield and mesons. Exciting phenomena appear at infinite coupling: the glueball superfield is no longer nilpotent and the classical chiral ring relations are quantum corrected by instanton operators bilinears. We also find expressions for the dressing of instanton operators of arbitrary charge. The same analysis is performed for $USp(2k)$ with an antisymmetric hypermultiplet and pure $SU(N)$ gauge theories.