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arXiv 0808.0506hep-th
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手征引力猜想的一个简单证明

A Simple Proof of the Chiral Gravity Conjecture

Andrew Strominger

摘要:

手征引力是三维渐近AdS 3引力,在耦合的临界值μ \ell =1处具有爱因斯坦、宇宙学和陈-西蒙斯项。通常,AdS 3引力的激发在由左移共形群和右移共形群组成的渐近对称群下进行非平凡变换。然而,最近在arXiv:0801.4566中证实,在手征点μ \ell =1处,所有激发都是手征的,因为它们仅在右移共形群下变换。我们在这里表明,在手征点,平凡的群的同态增强,包括左移动的共形变换,和渐近对称群只包含一个(右移动)副本的共形群。因此,双态不变性要求所有的物理激发都被左移共形变换湮灭,从而非微扰地建立了手征引力的手征性质。

英文摘要:

Chiral gravity is three-dimensional asymptotically AdS3 gravity with an Einstein, cosmological, and Chern-Simons term at a critical value of the coupling denoted μ\ell=1. Ordinarily, excitations of AdS3 gravity are known to transform non-trivially under an asymptotic symmetry group consisting of both a left-moving and a right-moving conformal group. However it was recently conjectured in arXiv:0801.4566 that at the chiral point μ\ell=1 all excitations are chiral in that they transform only under the right-moving conformal group. We show herein that at the chiral point, the group of trivial diffeomorphisms is enhanced to include the left-moving conformal transformations, and the asymptotic symmetry group contains only one (right-moving) copy of the conformal group. Diffeomorphism invariance then requires that all physical excitations are annihilated by left-moving conformal transformations, establishing nonperturbatively the chiral nature of chiral gravity.

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