Conical spaces, modular invariance and $c_{p,1}$ holography

Abstract

We propose a non-unitary example of holography for the family of two-dimensional logarithmic conformal field theories with negative central charge $c=c_{p,1}=-6p+13-6p^{-1}$. We argue that at large $p$, these models have a semiclassical gravity-like description which contains, besides the global AdS${}_3$ spacetime, a tower of solitonic solutions describing conical excess angles. Evidence comes from the fact that the central charge and the natural modular invariant partition function of such a theory coincide with those of the $c_{p,1}$ model. These theories have an extended chiral W-algebra whose currents have large spin of order $|c|$, and which in the bulk are realized as spinning conical solutions. As a by-product we also find a direct link between geometric actions for exceptional Virasoro coadjoint orbits, which describe fluctuations around the conical spaces, and Felder's free field construction of degenerate representations.

arXiv comment33 pages, 1 figure. V2: references added

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• 3D Gravity in a Box
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• A note on ensemble holography for rational tori
• AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants
• Higher-spin gauge theories in three spacetime dimensions
• Wormholes and surface defects in rational ensemble holography