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On the combinatorics of partition functions in AdS3/LCFT2

  • Yannick Mvondo-She
  • Konstantinos ZoubosEmail author
Open Access
Regular Article - Theoretical Physics
  • 43 Downloads

Abstract

Three-dimensional Topologically Massive Gravity at its critical point has been conjectured to be holographically dual to a Logarithmic CFT. However, many details of this correspondence are still lacking. In this work, we study the 1-loop partition function of Critical Cosmological Topologically Massive Gravity, previously derived by Gaberdiel, Grumiller and Vassilevich, and show that it can be usefully rewritten as a Bell polynomial expansion. We also show that there is a relationship between this Bell polynomial expansion and the plethystic exponential. Our reformulation allows us to match the TMG partition function to states on the CFT side, including the multi-particle states of t (the logarithmic partner of the CFT stress tensor) which had previously been elusive. We also discuss the appearance of a ladder action between the different multi-particle sectors in the partition function, which induces an interesting sl(2) structure on the n-particle components of the partition function.

Keywords

AdS-CFT Correspondence Classical Theories of Gravity Conformal and W Symmetry Conformal Field Models in String Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of PretoriaPretoriaSouth Africa
  2. 2.National Institute for Theoretical Physics (NITheP)GautengSouth Africa

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