Permutation orbifolds and holography

Abstract

Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold technology. In particular, we describe the group theoretic constraints on permutation groups to ensure a (stringy) holographic CFT. The primary result we uncover is that in order for the degeneracy of states to be finite in the large central charge limit, the groups of interest are the so-called oligomorphic permutation groups. Further requiring that the low-lying spectrum be sparse enough puts a bound on the number of orbits of these groups (on finite element subsets). Along the way we also study familiar cyclic and symmetric orbifolds to build intuition. We also demonstrate how holographic spectral properties are tied to the geometry of covering spaces for permutation orbifolds.

47 pages, 4 figures. v2: added comments. v3: minor improvements, published version

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• String Universality for Permutation Orbifolds
• Universality of Sparse $d>2$ Conformal Field Theory at Large $N$
• Charged structure constants from modularity
• High-Temperature Expansion of Supersymmetric Partition Functions
• Growing Extra Dimensions in AdS/CFT
• Modular crossings, OPE coefficients and black holes
• A conformal block Farey tail
• Chaos and pole skipping in CFT${}_2$
• Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
• Comments on the $S_N$ orbifold CFT in the large $N$-limit
• The Spectrum of Boundary States in Symmetric Orbifolds
• Emergent space-time and the supersymmetric index
• Stringy $\mathcal{N}=(2,2)$ holography for AdS${}_3$
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Holographic Calculation for Large Interval Rényi Entropy at High Temperature
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• Permutation Orbifolds and Chaos
• Scrambling time from local perturbations of the rotating BTZ black hole
• A Refined Count of BPS States in the D1/D5 System
• The Stranger Things of Symmetric Product Orbifold CFTs
• Small Black Holes and Near-Extremal CFTs
• The Holographic Landscape of Symmetric Product Orbifolds
• Siegel Modular Forms and Black Hole Entropy
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Topological modularity of Supermoonshine
• Transport across interfaces in symmetric orbifolds
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• Component twist method for higher twists in D1D5 CFT
• Siegel Paramodular Forms and Sparseness in AdS${}_3$/CFT${}_2$
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• The symmetric orbifold of N=2 minimal models
• Supersymmetric Landau-Ginzburg Tensor Models
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Free Fermion Cyclic/Symmetric Orbifold CFTs and Entanglement Entropy
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Limits of Vertex Algebras and Large N Factorization
• Rényi entropy of single-character CFTs on the torus