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arXiv 1808.03263hep-thgr-qc
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AdS $_3$引力的重参数化理论

A theory of reparameterizations for AdS$_3$ gravity

Jordan Cotler, Kristan Jensen

摘要:

我们将Chern-Simons对整体AdS $_3$和欧几里德BTZ黑洞的纯引力描述改写为AdS边界上的量子场论。由此得到的理论是Virasoro群的某个余伴轨道的路径积分量子化(两个副本),应视为边界引力子的量子场论。这个理论尊重所有的共形场论公理,除了一个:它不是模不变的。耦合常数是$1/c$,其中$c$是中心电荷,并且$1/c$中的微扰理论编码了引力对偶中的环贡献。QFT是一种类似于近似AdS $_2$引力的Schwarzian描述的重参数化理论,它具有以下几个特点:(i)它是紫外完备的;(ii)环面配分函数是真空Virasoro特征,它通过局部化变元是单圈精确的;(iii)它在紧化后简化为Schwarzian理论;(iv)它提供了一个强大的新工具,用于通过图形扩展来计算大$c$的Virasoro块。我们使用该理论来计算几个可观的一个循环顺序的散装,包括“重轻”限制的身份块。我们还对这个理论做了一些推广,包括描述双边永恒黑洞周围涨落的边界理论。

英文摘要:

We rewrite the Chern-Simons description of pure gravity on global AdS$_3$ and on Euclidean BTZ black holes as a quantum field theory on the AdS boundary. The resulting theory is (two copies of) the path integral quantization of a certain coadjoint orbit of the Virasoro group, and it should be regarded as the quantum field theory of the boundary gravitons. This theory respects all of the conformal field theory axioms except one: it is not modular invariant. The coupling constant is $1/c$ with $c$ the central charge, and perturbation theory in $1/c$ encodes loop contributions in the gravity dual. The QFT is a theory of reparametrizations analogous to the Schwarzian description of nearly AdS$_2$ gravity, and has several features including: (i) it is ultraviolet-complete; (ii) the torus partition function is the vacuum Virasoro character, which is one-loop exact by a localization argument; (iii) it reduces to the Schwarzian theory upon compactification; (iv) it provides a powerful new tool for computing Virasoro blocks at large $c$ via a diagrammatic expansion. We use the theory to compute several observables to one-loop order in the bulk, including the "heavy-light" limit of the identity block. We also work out some generalizations of this theory, including the boundary theory which describes fluctuations around two-sided eternal black holes.

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