Abstract
We propose an organizing principle for classifying and constructing Schrödinger-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 Schrödinger 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 β-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: 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 Schrödinger symmetry that are exact.
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Kraus, P., Perlmutter, E. Universality and exactness of Schrödinger geometries in string and M-theory. J. High Energ. Phys. 2011, 45 (2011). https://doi.org/10.1007/JHEP05(2011)045
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DOI: https://doi.org/10.1007/JHEP05(2011)045