Fermions in nonrelativistic AdS/CFT correspondence

Abstract

We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schr\"odinger group isometry. Although the boundary of the geometries with Schr\"odinger 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 nonrelativistic CFTs, though a nontrivial regularization may be needed.