Kerr/CFT, dipole theories and nonrelativistic CFTs

TL;DR

This work embeds Kerr/CFT within a string-theoretic framework by examining SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x K3. It identifies the dual field theories as DLCQs of the D1-D5 CFT deformed by a single (1,2) operator that is exactly marginal under the Schrödinger (nonrelativistic) conformal group, with finite right-moving temperature states corresponding to rotating extremal black holes. The study shows that many deformations preserve a Virasoro asymptotic symmetry with central charge equal to the undeformed case, and it connects Kerr/CFT to two-dimensional nonrelativistic CFTs via exact NR-CFT deformations. The results also illuminate dipole theories and their S-duals, clarify the role of three-dimensional Schrödinger spacetimes, and propose a concrete holographic dictionary at large N and strong coupling. Overall, the paper proposes NR-CFTs as a natural language for Kerr/CFT-like holography and outlines a program to compute correlators and entropy from the deformed D1-D5 CFT side.

Abstract

We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x U(1)^2 invariant deformations of AdS_3 x S^3 x 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 Schroedinger) group - which is simply SL(2,R)_L x 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 Schroedinger-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.

Figures (4)

• Figure 1: A family of $5d$ extremal charged, rotating black holes with the same value of $J_L$ and varying $Q$, which interpolates between the Myers-Perry black hole at $Q=0$ and the maximal value $Q^3 = J_L^{2}$. At precisely this point, the near horizon geometry becomes $AdS_3 \times S^2$ and the dual CFT description is well understood.
• Figure 2: The uplift of the one parameter family of black holes to six dimensions. Now the dual field theory can be understood at $\mathcal{O}(\epsilon)$ away from maximality by using AdS/CFT. Here $\epsilon \propto T_R$ labels both the temperature and the coefficient of the operator deformation.
• Figure 3: A different maximal limit of the six-dimensional geometries shows that all the black holes should be thought of as states of different temperatures inside the same field theory, which is a nonrelativistic CFT.
• Figure 4: Another descr‬iption of the family of black holes, now seen as having fixed $Q$ and varying $J_L$, as different thermal states with temperatures $T_Q$ in a nonrelativistic CFT. The lower bound on the angular momentum is $J_L^2 \geq Q^3$, so the Myers-Perry black hole is never a part of this family.