Narain to Narnia

Nathan Benjamin, Christoph A. Keller, Hirosi Ooguri, Ida G. Zadeh

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)425-470
Number of pages46
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Feb 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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