A note on ensemble holography for rational tori
Abstract
We study simple examples of ensembleaveraged holography in free compact boson CFTs with rational values of the radius squared. These wellknown rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the nonprimitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants.These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact U(1) × U(1) ChernSimons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS_{3} leads to the vacuum character of the chiral algebra. We also comment on wormholelike contributions to the multiboundary path integral.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2021
 DOI:
 10.1007/JHEP12(2021)177
 arXiv:
 arXiv:2110.08833
 Bibcode:
 2021JHEP...12..177R
 Keywords:

 AdSCFT Correspondence;
 Conformal Field Theory;
 Models of Quantum Gravity;
 High Energy Physics  Theory
 EPrint:
 21+6 pages. V2: minor corrections, published version