Schrodinger invariant solutions of M-theory with Enhanced Supersymmetry

TL;DR

The work addresses the challenge of realizing a gravity dual for a non-relativistic ABJM-like theory with enhanced ${\cal N}=2$ super-Schrödinger symmetry. By constructing the most general 11D supergravity solution compatible with ${\cal N}=2$ Schrodinger symmetry and global symmetries, the authors identify a one-parameter extension of the Ooguri–Park background and show that six supercharges can be preserved, but the remaining eight spectator supercharges cannot be accommodated under their assumptions. A no-go result for a fully symmetric NR-ABJM dual is established, and an uplift of a known IIB Schrödinger background to M-theory is analyzed for comparison. The findings suggest that either the NR-ABJM ground state breaks some symmetries or the background is obstructed by singularities or other constraints, guiding future holographic explorations of non-relativistic supersymmetric field theories.

Abstract

We find the most general solution of 11-dimensional supergravity compatible with N=2 super-Schrodinger symmetry with six supercharges and SU(2) x SU(2) x U(1) x Z_2 global symmetry. It can be viewed as a one-parameter extension of a recently constructed solution by Ooguri and Park. Our original motivation was to find the gravity dual of the non-relativistic ABJM theory. But, our analysis shows that no such solution exists within the reach of our assumptions. We discuss possible reasons for the non-existence of the desired solution. We also uplift a super-Schrodinger solution in IIB supergravity of Donos and Gauntlett to 11-dimension and comment on its properties.