Gravity duals for non-relativistic CFTs

TL;DR

This paper extends the AdS/CFT correspondence to non-relativistic conformal field theories with Galilean symmetry, constructing gravity duals that include pressureless dust and analyzing their holographic properties.

Contribution

It introduces a new class of gravity solutions with non-relativistic symmetries, including a bulk superconductor, and develops the holographic dictionary for these models.

Findings

Constructed metrics realizing Galilean invariance as isometries.

Solutions involve gravity coupled to pressureless dust, including a bulk superconductor.

Computed two-point correlators in the non-relativistic holographic setup.

Abstract

We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and compute some two-point correlators. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.