Fermions and the Sch/nrCFT Correspondence

TL;DR

This paper investigates Dirac fermions in Schr"odinger spacetime, analyzing their boundary two-point functions in the dual non-relativistic conformal field theory, and establishes a consistent renormalization procedure with Galilean invariant counterterms.

Contribution

It provides a detailed construction of the on-shell action for fermions in Schr"odinger spacetime and introduces a method for consistent boundary renormalization respecting Galilean symmetry.

Findings

Derived the boundary two-point function for fermionic operators.

Established a renormalization scheme with Galilean invariant counterterms.

Clarified the representation theory of the Schr"odinger algebra in this context.

Abstract

We consider the problem of Dirac fermions propagating on a spacetime of Schr\"odinger isometry and the associated boundary Euclidean two-point function of fermionic scaling operators of the holographic dual non-relativistic conformal theory. Paying careful attention to the representations of the Schr\"odinger algebra that appear in this problem, we show carefully how the on-shell action is constructed and how the boundary theory may be renormalized consistently by the inclusion of appropriate Galilean invariant boundary counterterms.