Coset Construction for Duals of Non-relativistic CFTs

TL;DR

This paper develops a systematic coset construction approach to identify and analyze holographic dual backgrounds for non-relativistic conformal field theories, including Schrödinger and Lifshitz geometries, demonstrating their uniqueness.

Contribution

It introduces a coset construction framework for non-reductive spaces and applies it to derive and prove the uniqueness of dual backgrounds for non-relativistic CFTs.

Findings

Reproduces known dual backgrounds for fermions at unitarity.

Shows the uniqueness of these dual backgrounds under physical assumptions.

Provides a unified organizational scheme for Schrödinger and Lifshitz geometries.

Abstract

We systematically analyze backgrounds that are holographic duals to non-relativistic CFTs, by constructing them as cosets of the Schrodinger group and variants thereof. These cosets G/H are generically non-reductive and we discuss in generality how a metric on such spaces can be determined from a non-degenerate H-invariant symmetric two-form. Applying this to the d=2 Schrodinger algebra, we reproduce the five-dimensional backgrounds proposed as duals of fermions at unitarity, and under reasonable physical assumptions, we demonstrate uniqueness of this background. The proposed gravity dual of the Lifshitz fixed-point, for which Galileian symmetry is absent, also fits into this organizational scheme and uniqueness of this background can also be shown.