Finite N Index and Angular Momentum Bound from Gravity

TL;DR

This paper calculates the finite N index and BPS partition functions for N=4 SYM in a new angular momentum limit derived from supergravity, revealing no finite N corrections to the index but corrections to the partition function.

Contribution

It introduces a novel maximal angular momentum limit from supergravity and computes the exact finite N index and partition functions in this regime.

Findings

Index remains unchanged at finite N.

Partition function receives finite N corrections.

New angular momentum limit arises from supergravity, not superconformal algebra.

Abstract

We exactly compute the finite N index and BPS partition functions for N=4 SYM theory in a newly proposed maximal angular momentum limit. The new limit is not predicted from the superconformal algebra, but naturally arises from the supergravity dual. We show that the index does not receive any finite N corrections while the free BPS partition function does.