The Stranger Things of Symmetric Product Orbifold CFTs

TL;DR

This paper investigates the unique behaviors of symmetric product orbifold conformal field theories under deformations, revealing unexpected growth patterns and classifying theories based on marginal operators and state sparseness.

Contribution

It provides the first classification of symmetric product orbifold theories according to deformation criteria and uncovers a new class with potential supergravity duals.

Findings

Identification of theories with Hagedorn-like growth despite having marginal operators.

Discovery of a new infinite class of theories satisfying both deformation criteria.

Insights into the behavior of light states and their implications for AdS/CFT correspondence.

Abstract

Symmetric product orbifold theories are valuable due to their universal features at large $N$. Here we will demonstrate that they have features that are not as pervasive: we provide evidence of strange behaviour under deformations within their moduli space. To this end, we consider the symmetric product orbifold of tensor products of $\mathcal{N}=2$ super-Virasoro minimal models, and classify them according to two criteria. The first criterion is the existence of a single-trace twisted exactly marginal operator that triggers the deformation. The second criterion is a sparseness condition on the growth of light states in the elliptic genera. In this context we encounter a strange variety: theories that obey the first criterion but the second criterion falls into a Hagedorn-like growth. We explain why this may be counter-intuitive and discuss how it might be accounted for in conformal perturbation theory. We also find a new infinite class of theories that obey both criteria, which are necessary conditions for each moduli space to contain a supergravity point.