NR $CFT_3$ duals in M-theory

TL;DR

This work extends NR CFT holography to $d=11$ supergravity by constructing warped $AdS_5$-type backgrounds with internal spaces that are $S^2$-bundles over $S^2 \times S^2$ or $S^2 \times T^2$ and seeks Schrödinger symmetry with $z=2$. Using flux decompositions $G=G_0+F$ and invariant flux ansätze on the external/internal sectors, the authors find that for the $S^2 \times S^2$ base only magnetic flux deformations are allowed, preserving two supersymmetries, while for $S^2 \times T^2$ the inclusion of electric fluxes yields a richer, generally non-supersymmetric landscape, including TsT-derived uplifts to IIB/M-theory. The analysis relies on the existing supersymmetric warped $AdS_5$ solutions of Gauntlett et al. and imposes Bianchi and equations of motion constraints to map the allowed deformations, illuminating the boundary between SUSY-preserving and SUSY-breaking NR CFT duals in this M-theory setup. The work also points to future directions such as five-dimensional consistent truncations and exploring NR duals at other dynamical exponents $z$, aiming to broaden the holographic toolkit for non-relativistic conformal field theories.

Abstract

We extend the search for supergravity solution duals of non-relativistic $d=3$ CFTs to $d=11$ supergravity. We consider the internal space to be an $S^2$ bundle over a product base: $S^2 \times S^2$ and $S^2 \times T^2$. For purely M-theoretic $S^2 \times S^2$, we find only magnetic fluxes preserving two supersymmetries. $S^2 \times T^2$ is far richer admitting in addition to magnetic fluxes, various non-trivial electric fluxes which break all supersymmetry.