弦和M理论中薛定谔几何的普适性和精确性
Universality and exactness of Schrodinger geometries in string and M-theory
摘要：
我们提出了一个组织原则，分类和构造薛定谔不变的解决方案在弦论和M-理论的基础上，这样的解决方案表示非线性完成的线性化矢量和引力子卡鲁扎-克莱因激发AdS紧化。一个重要的简化，来自AdS的对称性，是非线性只出现二次。相应地，每个AdS真空都允许由动力学指数z参数化的薛定谔变形的无限族。我们展示了容易找到这些解决方案，提出了三个新的结构：两个从M5膜，既包装和扩展，和一个从D1-D5（和S-对偶F1-NS 5）系统。从边界的角度来看，用零矢量算符扰动CFT可以导致自旋为2的算符的非零β函数;然而，对称性限制它们在耦合中至多是二次的。这种观点也使我们能够容易地证明非重整化定理：对于以上述方式构造的二阶导数超引力的任何Sch（z）解，如果变形KK模位于AdS超群的短多重态中，则z在高阶导数修正中不被修正到所有阶。此外，我们还找到了无穷多类具有4维、5维和7维Schrodinger对称性的1/4 BPS解的精确解.
英文摘要：
We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new constructions: two from M5 branes, both wrapped and extended, and one from the D1-D5 (and S-dual F1-NS5) system. From the boundary perspective, perturbing a CFT by a null vector operator can lead to nonzero beta-functions for spin-2 operators; however, symmetry restricts them to be at most quadratic in couplings. This point of view also allows us to easily prove nonrenormalization theorems: for any Sch(z) solution of two-derivative supergravity constructed in the above manner, z is uncorrected to all orders in higher derivative corrections if the deforming KK mode lies in a short multiplet of an AdS supergroup. Furthermore, we find infinite classes of 1/4 BPS solutions with 4-,5- and 7-dimensional Schrodinger symmetry that are exact.
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