Anisotropic flows into black holes

Abstract

We consider anisotropic black holes in the context of holographic renormalization group (RG) flows. We construct an a-function that is stationary at the boundary and the horizon and prove that it is also monotonic in both the exterior and the interior of the black hole. In spite of the reduced symmetry, we find that the “radial” null energy condition is sufficient to ensure the existence of this monotonic a-function. After constructing the a-function, we explore a holographic anisotropic p-wave superfluid state as a concrete example and numerical testing grounds. In doing so, we find that the a-function exhibits nontrivial oscillations in the trans-IR regime while preserving monotonicity. We find evidence that such oscillations appear to drive the trans-IR flow into nontrivial fixed points. We conclude by briefly discussing how our work fits into both the broader program of holographic RG flow and quantum information approaches to probing the black hole interior.

Bounding entanglement wedge cross sections

“…It is therefore important to test the validity of the proposed weak monogamy in other more involved string theory setups, such as in those where there is a non-trivial renormalization group flow [41,63,73]. Other interesting extensions would be to non-Lorentz invariant systems, e.g., to those possessing intrinsic anisotropy [74] or induced by an external control parameter [48,[75][76][77][78][79][80][81][82][83][84].…”