On the combinatorics of partition functions in AdS3/LCFT2

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.

26 pages. Typos fixed, references and clarifications added

References in corpus (14)

• Massive Gravity in Three Dimensions
• Three-Dimensional Gravity Revisited
• Counting Gauge Invariants: the Plethystic Program
• Topologically Massive Gravity and the AdS/CFT Correspondence
• Measurement of the charm fragmentation function in D* photoproduction at HERA
• Quantum W-symmetry in AdS_3
• Asymptotically anti-de Sitter spacetimes in topologically massive gravity
• Graviton 1-loop partition function for 3-dimensional massive gravity
• Erratum to `Instability in cosmological topologically massive gravity at the chiral point', arXiv:0805.2610
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators
• Generalised massive gravity one-loop partition function and AdS/(L)CFT
• Asymptotic counting of BPS operators in superconformal field theories
• On one-loop partition functions of three-dimensional critical gravities
• Multipartite Generating Functions and Infinite Products for Quantum Invariants

Cited by in corpus (9)

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• Shannon information entropy, soliton clusters and Bose-Einstein condensation in log gravity
• Moduli space of logarithmic states in critical massive gravities
• From Hurwitz numbers to Feynman diagrams: counting rooted trees in log gravity
• Fragmented perspective of self-organized criticality and disorder in log gravity
• On palindromic numerators of bigraded symmetric orbifold Hilbert series and Kostka-Foulkes polynomials
• Monodromy, Logarithmic Sectors, and Two-Point Functions in Critical Topologically Massive Gravity