Inductive calculation of superconformal indices based on giant graviton expansion

TL;DR

This paper develops an inductive method to calculate superconformal indices of certain ${ m N}=2$ theories using giant graviton expansion, providing new insights into their structure and constraints.

Contribution

It introduces a simple-sum giant graviton expansion approach that constrains and determines superconformal indices for ${ m N}=2$ theories on D3-branes.

Findings

Derived initial terms of superconformal indices for arbitrary rank N.

Established strong self-dual constraints on the indices.

Provided a new computational framework for superconformal indices.

Abstract

We investigate a simple-sum giant graviton expansion of the superconformal indices of ${\cal N}=2$ superconformal field theories realized on D3-branes probing $7$-brane backgrounds with constant axio-dilation field. The expansion is of self-dual type, and imposes strong constraints on the indices. By using the constraints we determine first few terms in the superconformal indices for arbitrary rank $N$.