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arXiv 1406.0505hep-th
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超引力局域化与量子$AdS_4/CFT_3$全息术

Localization in Supergravity and Quantum $AdS_4/CFT_3$ Holography

Atish Dabholkar, Nadav Drukker, Joao Gomes

摘要:

在Sasaki-Einstein流形$X_{7}$上通过一致截断得到的四维规范超引力中,利用局域化技术计算了M理论在$AdS_4 \times X_7 $上的量子引力配分函数.超引力路径积分简化为两个集体坐标上的有限维积分,从而参数化局域化瞬子解。离壳层瞬子解的重整化作用量线性地和全纯地依赖于在$AdS_{4}$中心计算的“平方根”预势。该配分函数类似于拓扑弦的波函数的拉普拉斯变换,并且在关于局部化积分的测度的假设下,产生与3-球上的边界ABJM理论的计算精确一致的Airy函数。我们的体量子引力计算在四维普朗克长度是非微扰精确的,但忽略了由于膜瞬子的修正。

英文摘要:

We compute the quantum gravity partition function of M-theory on $AdS_4 \times X_7 $ by using localization techniques in four-dimensional gauged supergravity obtained by a consistent truncation on the Sasaki-Einstein manifold $X_{7}$. The supergravity path integral reduces to a finite dimensional integral over two collective coordinates that parametrize the localizing instanton solutions. The renormalized action of the off-shell instanton solutions depends linearly and holomorphically on the "square root" prepotential evaluated at the center of $AdS_{4}$. The partition function resembles the Laplace transform of the wave function of a topological string and with an assumption about the measure for the localization integral yields an Airy function in precise agreement with the computation from the boundary ABJM theory on a 3-sphere. Our bulk quantum gravity computation is nonperturbatively exact in four-dimensional Planck length but ignores corrections due to brane-instantons.

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