Towards a gravity dual of the unitary Fermi gas

TL;DR

The work tackles the problem of a gravity dual for the unitary Fermi gas, a strongly coupled NRCFT with Schrödinger symmetry, by combining a large-$N$ extension with null dimensional reduction inspired by AdS/CFT approaches. It develops a framework connecting non-relativistic fermions to relativistic higher-spin theories via a dimensional reduction, and identifies a candidate bulk dual as the null-reduced Vasiliev theory on $\text{AdS}_{d+3}$ with $\mathfrak{u}(2)$-valued fields, appropriate boundary conditions, and a mass $m^2=-2d$ for bulk scalars. The paper outlines the symmetry structure, the coupling of fermion bilinears to sources, and the holographic dictionary needed to map boundary currents to bulk higher-spin fields, thereby providing a concrete semi-classical holographic description for unitary fermions. If realized, this construction offers a principled route to compute strongly coupled NRCFT observables using higher-spin gravity techniques and deepens the link between non-relativistic conformal physics and holography.

Abstract

Inspired by the method of null dimensional reduction and by the holographic correspondence between Vasiliev's higher-spin gravity and the critical O(N) model, a bulk dual of the unitary and the ideal non-relativistic Fermi gases is proposed.