We test some recent conjectures about extremal selfdual CFT's, which are the candidate holographic duals of pure gravity in AdS_3. We prove that no c= 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic \mu due to negative-energy massive gravitons. However at the critical value \mu\ell=1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by \ell M=J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c_L,c_R)=(0,3\ell /G).
For pure gravity in AdS_3, Witten has given a recipe for the construction of holomorphically factorizable partition functions of pure gravity theories with central charge c=24k. The partition function was found to be a polynomial in the modular invariant j-function. We show that the partition function can be obtained instead as a modular sum which has a more physical interpretation as a sum over geometries. We express both the j-function and its derivative in terms of such a sum.
難しい話題なのに、何故かアクセス集中している．
返信削除arXiv:0801.0988v1 [hep-th] 7 Jan 2008
返信削除Monster symmetry and Extremal CFTs
Davide Gaiotto
Abstract
We test some recent conjectures about extremal selfdual CFT's, which are the candidate holographic duals of pure gravity in AdS_3. We prove that no c= 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
arXiv:0801.4566 [hep-th]
返信削除Chiral Gravity in Three Dimensions
Wei Li, Wei Song, Andrew Strominger
Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic \mu due to negative-energy massive gravitons. However at the critical value \mu\ell=1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by \ell M=J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c_L,c_R)=(0,3\ell /G).
AdS_3 Partition Functions Reconstructed
返信削除arXiv:0707.1159v2
Manschot
For pure gravity in AdS_3, Witten has given a recipe for the construction of holomorphically factorizable partition functions of pure gravity theories with central charge c=24k. The partition function was found to be a polynomial in the modular invariant j-function. We show that the partition function can be obtained instead as a modular sum which has a more physical interpretation as a sum over geometries. We express both the j-function and its derivative in terms of such a sum.
Wikipedia Monstous Mooshineに、記事としてWittenの論文を付け加えたら、『量子重力との予想される関係』という独立した章立てにした方がおられる．ありがたい話だ．文献を追加しておいた．
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