The Stranger Things of Symmetric Product Orbifold CFTs

Abstract

Symmetric product orbifold theories are valuable due to their universal features at large $N$. Here we will demonstrate that they have features that are not as pervasive: we provide evidence of strange behaviour under deformations within their moduli space. To this end, we consider the symmetric product orbifold of tensor products of $\mathcal{N}=2$ super-Virasoro minimal models, and classify them according to two criteria. The first criterion is the existence of a single-trace twisted exactly marginal operator that triggers the deformation. The second criterion is a sparseness condition on the growth of light states in the elliptic genera. In this context we encounter a strange variety: theories that obey the first criterion but the second criterion falls into a Hagedorn-like growth. We explain why this may be counter-intuitive and discuss how it might be accounted for in conformal perturbation theory. We also find a new infinite class of theories that obey both criteria, which are necessary conditions for each moduli space to contain a supergravity point.

34 pages, 3 figures, v3: minor changes, version as published in JHEP

References in corpus (9)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• String Universality for Permutation Orbifolds
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• Permutation orbifolds and holography
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Universal lifting in the D1-D5 CFT
• The Holographic Landscape of Symmetric Product Orbifolds

Cited by in corpus (10)

• Transport across interfaces in symmetric orbifolds
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Coupled minimal models revisited II: Constraints from permutation symmetry
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Conformal field theories dual to quantum gravity with strongly coupled matter
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• A New Supersymmetry Index for the D1-D5 CFT
• Searching for strongly coupled AdS matter with multi-trace deformations
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality