Narain to Narnia

Abstract

We generalize the holographic correspondence between topological gravity coupled to an abelian Chern-Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi-Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.

27 pages + appendices, 4 figures; v2: minor changes

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Cited by in corpus (17)

• Solving 3d Gravity with Virasoro TQFT
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Disorder Averaging and its UV (Dis)Contents
• Holographic description of Narain CFTs and their code-based ensembles
• TQFT gravity and ensemble holography
• Comments on Summing over Bordisms in TQFT
• Euclidean wormholes in two-dimensional CFTs from quantum chaos and number theory
• Weighed average over Narain moduli space as $T\bar{T}$ deformation of CFT target space
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Classical geometry from the tensionless string
• Wormholes and surface defects in rational ensemble holography
• Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited
• (Half) Wormholes under Irrelevant Deformation
• A Tale of Two Saddles
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories
• Factorization and global symmetries in holography
• A universal sum over topologies in 3d gravity