The Holographic Landscape of Symmetric Product Orbifolds

TL;DR

This paper analyzes the growth of elliptic genus coefficients in symmetric product orbifolds, distinguishing between stringy and supergravity regimes, and proposes a diagnostic to classify these theories, suggesting new AdS3/CFT2 dualities.

Contribution

It introduces a diagnostic to classify symmetric product orbifolds into stringy or supergravity regimes and constructs elliptic genera with supergravity-like growth, indicating new AdS3/CFT2 dualities.

Findings

Growth of low energy states can be Hagedorn or slower, indicating stringy or supergravity duals.

Constructed elliptic genera with supergravity-like growth, suggesting new AdS3/CFT2 realizations.

Provided exact BPS degeneracies matching supergravity spectra.

Abstract

We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. We find that this landscape decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS$_3$. We provide a simple diagnostic which places any symmetric product orbifold in either region. We construct a class of elliptic genera with such supergravity-like growth, indicating the possible existence of new realizations of AdS$_3$/CFT$_2$ where the bulk is a semi-classical supergravity theory. In such cases, we give exact expressions for the BPS degeneracies, which could be matched with the spectrum of perturbative states in a dual supergravity description.