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 Schrödinger group isometry. Although the boundary of the geometries with Schrödinger 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.

Schrödinger Fermi liquids

“…We notice the boundary actionψψ, due to the Γ τ form; it couples the first component of the spinor ψ to the third component of ψ, which couples the second component of ψ to the fourth component of ψ. Both two-point function or ψψ shows r 2ν þ scaling in [27] and [28] and our work. However, the r 2ν − scaling is only seen in our and the Green's functions of [28].…”

“…Notably, the conformal dimension of NRCFT here depends on the mass operator M, which is quite different from CFT. More peculiarly, the conformal dimension for spinors has an extra m AE 1 2 split, as already noticed in [27,28]. In the following we denote dimension d as the spatial dimension of x 1 ; x 2 ; …; x d .…”

“…The asymptotic Schrödinger bulk spacetime is denoted as Schr dþ3 (distinguished from the AdS dþ2 ), where as the corresponding boundary theory of Schr dþ3 is NRCFT dþ1 (CFT dþ1 for AdS dþ2 ). We summarize the conformal dimensions of the spin-0 boson [30] and spin-1=2 fermion operator ( [27,28]) in Table I.…”

“…Its gravity dual theory had been proposed, with solutions of zero temperature pure Schrödinger (Schr) geometry [20,21], finite temperature black holes [22][23][24], and charged black holes [25,26]. There has been some pursuits on studying fermions in this asymptotic Schrödinger geometry [27][28][29]. However, to our knowledge, the holographic study of the Fermi surface from strongly interacting fermions with NRCFT background has not yet been explored in the literature.…”

Holographic superconductor developed in BTZ black hole background with backreactions

“…Recently attempts to study the holographic superconductor away from the probe limit by considering the backreaction have been carried out in [25]- [36].…”