Kerr/CFT, dipole theories and nonrelativistic CFTs

Abstract

Abstract We study solutions of type IIB supergravity which are SL(2, $\mathbb{R}$ ) × SU(2) × U(1)2 invariant deformations of AdS 3 × S 3 × K3 and take the form of products of self-dual spacelike warped AdS 3 and a deformed three-sphere. One of these backgrounds has been recently argued to be relevant for a derivation of Kerr/CFT from string theory, whereas the remaining ones are holographic duals of two-dimensional dipole theories and their S-duals. We show that each of these backgrounds is holographically dual to a deformation of the DLCQ of the D1-D5 CFT by a specific supersymmetric (1,2) operator, which we write down explicitly in terms of twist operators at the free orbifold point. The deforming operator is argued to be exactly marginal with respect to the zero-dimensional nonrelativistic conformal (or Schrödinger) group — which is simply SL(2, $\mathbb{R}$ ) L  × U(1) R . Moreover, in the supergravity limit of large N and strong coupling, no other single-trace operators are turned on. We thus propose that the field theory duals to the backgrounds of interest are nonrelativistic CFTs defined by adding the single Scrödinger-invariant (1, 2) operator mentioned above to the original CFT action. Our analysis indicates that the rotating extremal black holes we study are best thought of as finite right-moving temperature (non-supersymmetric) states in the above-defined supersymmetric nonrelativistic CFT and hints towards a more general connection between Kerr/CFT and two-dimensional non-relativistic CFTs.