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.

arXiv comment29 pages, 1 figure; v2 references added

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• $\mathcal{N}=(2,2)$ AdS${}_3$ from D3-branes wrapped on Riemann surfaces
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• The Stranger Things of Symmetric Product Orbifold CFTs
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• Transport across interfaces in symmetric orbifolds
• A New Supersymmetry Index for the D1-D5 CFT
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• The Resolved Elliptic Genus and the D1-D5 CFT