Superconformal indices for non-Lagrangian theories in five dimensions

TL;DR

This paper introduces two new methods to compute superconformal indices for five-dimensional non-Lagrangian theories, utilizing brane web transitions and orientifold plane relationships, enabling analysis of theories lacking conventional descriptions.

Contribution

The paper presents two innovative techniques for calculating superconformal indices of 5d non-Lagrangian theories, expanding computational tools for these complex models.

Findings

Computed indices for all known rank-1 non-Lagrangian theories

Identified flavor symmetries and their global forms at CFT fixed points

Demonstrated the effectiveness of brane web and orientifold methods

Abstract

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O$7^+$-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points.