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 AdS3. 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 AdS3/CFT2 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.
Highlights
In this work, we will address this question in the context of AdS3/CFT2
We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge
We considered the landscape of two-dimensional SCFTs that are given by symmetric product orbifolds
Summary
Our objective should be clear: we want to scan the space of CFT2 with a large central charge and ask whether the low-lying spectrum is supergravity-like. We will provide a classification of the seed theories C that divides them into two classes: Hagedorn Landscape: Supersymmetric examples of symmetric product orbifold theories whose light BPS states have Hagedorn growth as defined above These instances have less utility in a gravitational context since they will never admit a supergravity growth via a marginal deformation, albeit there might be other interesting CFT or string theory applications of them. This is the most typical situation within the space of symmetric product orbifolds. The detailed analysis of the mathematical techniques to extract the light spectrum is given in a companion paper [13]
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