Symmetries and currents of the ideal and unitary Fermi gases

TL;DR

This paper explores the infinite-dimensional symmetry algebra of free Fermi gases, its relation to higher-spin theories, and discusses potential holographic dualities for these non-relativistic systems.

Contribution

It identifies the maximal symmetry algebra of free Fermi gases as a non-relativistic higher-spin algebra and connects it to holographic duality frameworks.

Findings

Derived infinite collection of Noether currents from relativistic counterparts.

Reformulated minimal coupling of currents using Weyl quantisation.

Discussed potential holographic duals for ideal and unitary Fermi gases.

Abstract

The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite dimensional extension of the Schroedinger algebra, it is isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. The associated infinite collection of Noether currents bilinear in the fermions are derived from their relativistic counterparts via a light-like dimensional reduction. The minimal coupling of these currents to background sources is rewritten in a compact way by making use of Weyl quantisation. Pushing forward the similarities with the holographic correspondence between the minimal higher-spin gravity and the critical O(N) model, a putative bulk dual of the unitary and the ideal Fermi gases is discussed.