Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry

TL;DR

This paper explores a geometric model realizing Schroedinger symmetry in spacetime, proposing a holographic duality with nonrelativistic fermionic systems and discussing implications for nonrelativistic holography.

Contribution

It introduces a geometric realization of Schroedinger symmetry as a spacetime symmetry and connects it to nonrelativistic fermionic theories via holography.

Findings

Schroedinger symmetry can be realized geometrically in a spacetime model.

Free fermions and fermions at unitarity correspond to the same bulk theory with different boundary conditions.

Extended nonrelativistic coordinate invariance is realized holographically.

Abstract

We discuss a realization of the nonrelativistic conformal group (the Schroedinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.