A note on instanton operators, instanton particles, and supersymmetry

TL;DR

The paper resolves an apparent tension between instanton operators in 5d SUSY gauge theories and their role in the superconformal index by showing that instanton operators come in a one-parameter family labeled by $\rho$, with SUSY preserved only in the pointlike limits $\rho\to 0$ or $\infty$. In these limits flux concentrates at a pole, producing supersymmetric, BPST-like instantons that match the states counted by the index and the expected fermionic zero-mode structure. The analysis connects operator insertions to instanton particles and to the broken current multiplet arising from fermionic zero modes, while situating these results in the context of UV fixed points and dimensional uplifts to 6d. Overall, the work clarifies how instanton operators, instanton states, and zero-mode counting coherently determine the BPS spectrum and index in 5d gauge theories.

Abstract

We clarify certain aspects of instanton operators in five-dimensional supersymmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states contributing to the index as well as with the zero mode counting leading to broken current multiplets.