Averaging over Narain moduli space

Alexander Maloney, Edward Witten

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

Abstract

Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

Original languageEnglish (US)
Article number187
JournalJournal of High Energy Physics
Volume2020
Issue number10
DOIs
StatePublished - Oct 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Keywords

  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Gauge-gravity correspondence

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