Towards a bulk dual of the unitary Fermi gas
Relativistic O(N)-like and non-relativistic BCS-like models are double-trace deformations of free theories and therefore share many similarities. A uniform treatment of their connected correlator generating functionals of local bilinear operators is performed. Moreover, the maximal algebra of symmetries of the free Schroedinger equation is determined. This algebra of symmetries is an infinite-dimensional extension of the Schroedinger algebra, isomorphic to the Weyl algebra of quantum observables, and it may be interpreted as a non-relativistic higher-spin algebra. Pushing forward the similarities with the holographic correspondence between Vasiliev higher-spin gravity and the critical O(N) model, suggests a putative bulk dual of the unitary and the ideal Fermi gases.