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• W2188950892 abstract "We begin by discussing the basic features of pure 2+1 dimensional gravity. Then we set the value of the cosmological constant to be negative, regime in which the BTZ black hole and the Brown-Henneaux excitations arise. We discuss the general geometric framework for these theories and find non-classical restrictions on the value of the cosmological constant. Following [hep-th/07120155], we attempt to build the modular invariant partition functions of the CFT dual of pure 2+1 gravity. We do this by summing classical geometries over the orbits of the group Γ∞ PSL(2,Z). It turns out that the result obtained cannot be interpreted as the partition function of a conformal field theory. Subsequently we discuss the proposal made in [hep-th/07063359] in which the CFT dual is identified with an Extremal CFT (ECFT) with central charge c = 24k. For the case c = 24, the resulting CFT is the so-called Monster Module M whose partition function is known to be the J-function. Afterwards, we show how to compute the partition functions for k ∈ Z using only the constraints imposed by modular invariance and holomorphic factorization. Then we show that the entropies derived from these partition functions are in good agreement with the Bekenstein-Hawking entropy of the BTZ black hole. The result, although appealing, is still based on rather speculative grounds, since the existence of c > 24 ECFT’s is still uncertain." @default.
• W2188950892 created "2016-06-24" @default.
• W2188950892 creator A5008703922 @default.
• W2188950892 date "2008-01-01" @default.
• W2188950892 modified "2023-09-26" @default.
• W2188950892 title "Modular invariance and 3D Gravity" @default.
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• W2188950892 hasPublicationYear "2008" @default.
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