Universality and exactness of Schrodinger geometries in string and M-theory

TL;DR

This paper classifies and constructs Schrödinger-invariant solutions in string and M-theory, revealing their relation to AdS compactifications and demonstrating the existence of exact, supersymmetric solutions with various dimensions.

Contribution

It introduces a new organizing principle for Schrödinger solutions, provides explicit constructions from M5 branes and D1-D5 systems, and proves nonrenormalization theorems for these solutions.

Findings

Infinite families of Schrödinger deformations exist for any AdS vacuum.

Explicit solutions from M5 branes and D1-D5 systems are constructed.

Certain supersymmetric solutions are shown to be exact and uncorrected by higher derivative terms.

Abstract

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.