Universality and exactness of Schrodinger geometries in string and M-theory
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(Feb 8, 2011)

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. From the boundary perspective, perturbing a CFT by a null vector operator generically leads to nonzero beta-functions for spin-2 operators. Symmetry restricts them to be at most quadratic in couplings, and the Galilean-symmetric RG fixed point can be found explicitly. 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. This point of view also allows us to easily prove nonrenormalization theorems: to every Kaluza-Klein vector and graviton that lies in a short multiplet of an AdS supergroup, there exists at least one Sch(z) solution in which z is uncorrected to all orders in higher derivative corrections. 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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