Schrödinger Deformations of AdS_3 x S^3

TL;DR

This work constructs and analyzes Schrödinger-invariant deformations of the IIB near-horizon background $AdS_3\times S^3\times T^4$, yielding an infinite class of solutions with both integer and half-integer dynamical exponents $n$. The deformations are encoded by a transverse vector harmonic $\mathcal{A}$ on $S^3$ and a scalar function $\Omega$, with the equations of motion reducing to Laplace-type problems on the three-sphere; explicit $n=2$ and $n=3$ solutions are worked out and a general method for arbitrary $n$ is given. Supersymmetry analysis shows that many solutions preserve four supercharges (1/4 BPS) in the $\mathcal{A}=0$ sector or for special $n=2$ parameter choices, while most cases with $\mathcal{A}\neq0$ and $n>2$ are non-supersymmetric. In the dual D1-D5 (or F1-NS5) CFT, these backgrounds correspond to constant null sources for irrelevant vector and spin-2 operators with dimensions $\Delta_{\text{vector}}=1+n$ and $\Delta_{\text{spin-2}}=l+2$, revealing a controlled holographic realization of non-relativistic, scale-invariant deformations in two-dimensional boundary theories. The results open avenues for exploring non-AdS holography, stability, and potential exact worldsheet or dipole-theory interpretations.

Abstract

We study Schrödinger invariant deformations of the AdS_3 x S^3 x T^4 (or K3) solution of IIB supergravity and find a large class of solutions with integer and half-integer dynamical exponents. We analyze the supersymmetries preserved by our solutions and find an infinite number of solutions with four supersymmetries. We study the solutions holographically and find that the dual D1-D5 (or F1-NS5) CFT is deformed by irrelevant operators of spin one and two.