Holographic RG flow dual to attractor flow in extremal black holes

TL;DR

This paper explores the holographic duality between extremal black holes and two-dimensional field theories using RG flow techniques, linking attractor mechanisms to fixed points in the dual theory.

Contribution

It extends holographic RG flow analysis to extremal black holes, connecting attractor flows with dual 2D field theory RG flows and calculating central charges.

Findings

Holographic RG flow equations match attractor flow equations.

Central charge and c-function are derived from gravity and anomaly calculations.

Attractor fixed points correspond to RG flow fixed points in the dual theory.

Abstract

We extend the discussion of the "Kerr/CFT correspondence" and its recent developments to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow. It is conjectured that the extremal black hole space-time is holographically dual to the chiral two dimensional field theory. Our example is a typical four dimensional Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on four cycles of Calabi-Yau threefold. In five dimensional supergravity view point this near horizon geometry is $AdS_3\times S^2$, and three dimensional gravity coupled to moduli fields is effectively obtained after a dimensional reduction on $S^2$. Constructing the Hamilton-Jacobi equation, we define the holographic RG flow from the three dimensional gravity. The central charge of the Virasoro algebra is calculable from the conformal anomaly at the point where the beta function defined from gravity side becomes zero. In general, we can also identify the c-function of the dual two dimensional field theory. We show that these flow equations are completely equivalent to not only BPS but also non-BPS attractor flow equations of the muduli fields. The attractor mechanism by which the values of the moduli fields are fixed at the event horizon of the extremal black hole can be understood equivalently to the fact that the RG flows are fixed at the critical points in the dual field theory.