On the combinatorics of partition functions in AdS3/LCFT2

Yannick Mvondo-She (Department of Physics, University of Pretoria, Private Bag X20, Hatfield, Pretoria, 0028, South Africa; National Institute for Theoretical Physics (NITheP), Gauteng, South Africa) ; Konstantinos Zoubos (Department of Physics, University of Pretoria, Private Bag X20, Hatfield, Pretoria, 0028, South Africa; National Institute for Theoretical Physics (NITheP), Gauteng, South Africa)

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.

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      "surname": "Zoubos", 
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      "source": "Springer", 
      "value": "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."
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Published on:
17 May 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 5
Pages 1-30
DOI:
https://doi.org/10.1007/JHEP05(2019)097
arXiv:
1811.08144
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

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