5-dim Superconformal Index with Enhanced En Global Symmetry

TL;DR

This paper computes the superconformal index for 5D Sp(1) gauge theories, confirming the enhancement of global symmetry to E_{N_f+1} at strong coupling for N_f ≤ 5, using localization methods.

Contribution

It provides the first detailed calculation of the superconformal index for these theories, demonstrating symmetry enhancement and addressing instanton contributions.

Findings

Confirmed symmetry enhancement to E_{N_f+1} for N_f ≤ 5

Calculated perturbative and instanton contributions to the index

Identified issues in instanton pole structures for N_f=6,7 cases

Abstract

The five-dimensional $\mathcal{N}=1$ supersymmetric gauge theory with Sp(N) gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes with $N_f$ D8-branes on top of a single O8 orientifold plane in Type I' theory. This theory is known to be superconformal at the strong coupling limit with the enhanced global symmetry $E_{N_f+1}$ for $N_f\le 7$. In this work we calculate the superconformal index on $S^1\times S^4$ for the Sp(1) gauge theory by the localization method and confirm such enhancement of the global symmetry at the superconformal limit for $N_f\le 5$ to a few leading orders in the chemical potential. Both perturbative and (anti)instanton contributions are present in this calculation. For $N_f=6,7$ cases some issues related the pole structure of the instanton calculation could not be resolved and here we could provide only some suggestive answer for the leading contributions to the index. For the Sp(N) case, similar issues related to the pole structure appear.