Asymptotic counting of BPS operators in superconformal field theories

TL;DR

This paper analyzes the asymptotic behavior of BPS operator counting in superconformal field theories, revealing factorization properties and large N limit structures relevant for holography.

Contribution

It derives asymptotic formulas for multi-variable partition functions counting BPS operators and explores their factorization and large N limit properties.

Findings

Asymptotic density of states formulas for BPS operators

Factorization property of finite N partition functions

Introduction of a limit curve concept related to holography

Abstract

We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For non-zero coupling, the corresponding multi-variable partition functions can be written in terms of generating functions for vector partitions or their weighted generalisations. We derive asymptotics for the density of states for a wide class of such multi-variable partition functions. We also point out a particular factorisation property of the finite N partition functions. Finally, we discuss the concept of a limit curve arising from the large N partition functions, which is related to the notion of a typical state and discuss some implications for the holographic duals.