Localization in supergravity and quantum AdS 4 /CFT3 holography
Localization in supergravity and quantum AdS 4 /CFT3 holography
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超重力和量子 AdS 4 /CFT3 全息术中的定位
DOI：
10.1007/jhep10(2014)090
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发表时间：
2014
影响因子：
5.4
通讯作者：
Dabholkar A
中科院分区：
文献类型：
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作者：
Dabholkar A
利用Sasaki-Einstein流形X7上一致截断得到的四维规范超引力中的局域化技术，计算了AdS 4× X7上M理论的量子引力配分函数.超重力路径积分减少到一个有限维积分超过两个集体坐标，参数化的局域化瞬子解决方案。重正化作用的离壳瞬子的解决方案依赖于线性和全纯的“平方根”prepotential评估中心的AdS 4。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量的假设下，产生与3-球面上的边界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。
We compute the quantum gravity partition function of M-theory on AdS 4× 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.