Galilean conformal algebra in two dimensions and cosmological topologically massive gravity
Galilean conformal algebra in two dimensions and cosmological topologically massive gravity
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DOI：
10.1016/j.nuclphysb.2010.05.015
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发表时间：
2010-03
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影响因子：
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通讯作者：
Kyosuke Hotta;T. Kubota;T. Nishinaka
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文献类型：
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作者：
Kyosuke Hotta;T. Kubota;T. Nishinaka
我们考虑一个特殊的三维引力理论，即所谓的宇宙拓扑大质量引力（CTMG），它包括引力Chern-Simons项和负宇宙常数的AdS边界上的二维时空中的伽利略共形代数（GCA）的实现。二维的无限维GCA是从相对论CFT的Virasoro代数通过取标度极限t→t，x→ λ x，λ →0得到的。母相对论性CFT应该有O（1/1）阶的左右中心电荷，但在极限1 →0时符号相反。另一方面，根据Brown-Henneaux的分析，Virasoro代数在AdS 3的边界上实现，但左右中心荷的不对称性仅与引力Chern-Simons耦合因子1/μ有关。如果μ在相应的极限下为O（λ）阶，则在体CTMG的AdS边界上存在非平凡中心的GCA.在此基础上，我们从体黑洞熵出发，给出了伽利略场论的一个新的熵公式，它是Cardy公式的非相对论对应。本文还讨论了微态计数法能否重现这种现象。
We consider a realization of the Galilean conformal algebra (GCA) in two-dimensional space–time on the AdS boundary of a particular three-dimensional gravity theory, the so-called cosmological topologically massive gravity (CTMG), which includes the gravitational Chern–Simons term and the negative cosmological constant. The infinite-dimensional GCA in two dimensions is obtained from the Virasoro algebra for the relativistic CFT by taking a scaling limit t→t, x→ϵx with ϵ→0. The parent relativistic CFT should have left and right central charges of order O(1/ϵ) but opposite in sign in the limit ϵ→0. On the other hand, by Brown–Henneaux's analysis the Virasoro algebra is realized on the boundary of AdS3, but the left and right central charges are asymmetric only by the factor of the gravitational Chern–Simons coupling 1/μ. If μ behaves as of order O(ϵ) under the corresponding limit, we have the GCA with non-trivial centers on AdS boundary of the bulk CTMG. Then we present a new entropy formula for the Galilean field theory from the bulk black hole entropy, which is a non-relativistic counterpart of the Cardy formula. It is also discussed whether it can be reproduced by the microstate counting.