Families of IIB duals for nonrelativistic CFTs

TL;DR

Hartnoll and Yoshida develop a broad holographic framework for nonrelativistic CFTs by constructing a 21-parameter family of IIB Schrödinger backgrounds obtained from $AdS_5\times X_5$ via a harmonic profile $f(X_5)$, with or without NSNS flux. The dynamical exponent $z$ is tied to eigenvalues of the internal Laplacian, and the backgrounds include near-horizon branewave realizations with $F_5$ and $B_2$ flux enabling interpolation between fluxless and flux backgrounds. They show that scalar fluctuations effectively renormalize KK masses, identify a stability/instability hypersurface where long-wavelength modes destabilize the spacetime, and derive a range of $z\neq 2$ backgrounds. The work also constructs RG flows and Coulomb-branch deformations that asymptote to Schrödinger geometries for different internal symmetries, suggesting a versatile holographic toolkit for 2+1D nonrelativistic quantum critical systems and potential DLCQ interpretations of ${\cal N}=4$ SYM.

Abstract

We show that the recent string theory embedding of a spacetime with nonrelativistic Schrodinger symmetry can be generalised to a twenty one dimensional family of solutions with that symmetry. Our solutions include IIB backgrounds with no three form flux turned on, and arise as near horizon limits of branewave spacetimes. We show that there is a hypersurface in the space of these theories where an instability appears in the gravitational description, indicating a phase transition in the nonrelativistic field theory dual. We also present simple embeddings of duals for nonrelativistic critical points where the dynamical critical exponent can take many values z \neq 2.