Fermions in non-relativistic AdS/CFT correspondence

TL;DR

This paper extends the AdS/CFT correspondence to include fermionic fields in non-relativistic settings, analyzing two-point functions of fermionic operators using geometries with Schrödinger symmetry.

Contribution

It introduces a method to study fermionic operators in non-relativistic CFTs via geometries with Schrödinger symmetry, expanding the holographic dictionary.

Findings

Two-point functions match expected non-relativistic CFT form

Fermionic propagators can be computed in Schrödinger geometries

Regularization may be necessary for precise results

Abstract

We extend the non-relativistic AdS/CFT correspondence to the fermionic fields. In particular we study the two point function of a fermionic operator in non-relativistic CFTs by making use of a massive fermion propagating in geometries with Schrodinger group isometry. Although the boundary of the geometries with Schrodinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in non-relativistic CFTs, though a non-trivial regularization may be needed.