Higgs branch of 5d $\mathcal{N}=1$ symplectic gauge theories and dressed instanton operators

TL;DR

This paper analyzes the Higgs branch of 5d $ N=1$ $Sp(k)$ gauge theories, revealing how the chiral ring decomposes into instanton sectors and how dressing factors encode finite coupling effects.

Contribution

It introduces a new framework for expressing the Higgs branch chiral ring as a product of instanton contributions and dressing factors, extending understanding of instanton operators in 5d theories.

Findings

Decomposition of the chiral ring into instanton sectors.

Identification of a universal dressing factor.

Insight into finite coupling effects on the Higgs branch.

Abstract

We expand in instanton charge sectors the representation content of the infinite coupling chiral ring of the Higgs branch of 5d $\mathcal{N}=1$ $Sp(k)$ theories with $N_f$ flavours. The entire chiral ring can be expressed as the product of bare instantons, one for each topological sector, times a common dressing factor depending on the mesons and the instanton-anti instanton bound state. The dressing factor, which is independent of the instanton number, encodes the chiral ring of the theory at finite coupling with one additional colour.