The Holographic Landscape of Symmetric Product Orbifolds

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.

29 pages, 1 figure; v2 references added

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• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• F-theory and AdS_3/CFT_2
• Supersymmetric AdS_3 solutions of type IIB supergravity
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Cited by in corpus (1)

• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$