Conformal Symmetry for Black Holes in Four Dimensions and Irrelevant Deformations

TL;DR

This paper demonstrates how irrelevant deformations in a dual CFT can dynamically generate subtracted geometries of four-dimensional black holes, linking conformal symmetry, flow construction, and holographic interpretations.

Contribution

It introduces a dynamic flow approach to implement conformal factor replacement and identifies the dual operators responsible for irrelevant perturbations in the CFT.

Findings

Constructed an explicit interpolating flow for static black holes.

Linked the flow to irrelevant operators in the dual CFT.

Provided a framework for computing corrections to CFT results.

Abstract

It has been argued several times in the past that the structure of the entropy formula for general non-extremal asymptotically flat black holes in four dimensions can be understood in terms of an underlying conformal symmetry. A recent implementation of this idea, carried out by Cveti\v{c} and Larsen, involves the replacement of a conformal factor in the original geometry by an alternative conformal factor in such a way that the near-horizon behavior and thermodynamic properties of the black hole remain unchanged, while only the asymptotics or "environment" of the geometry are modified. The solution thus obtained, dubbed "subtracted geometry", uplifts to an asymptotically AdS$_{3}\times S^{2}$ black hole in five dimensions, and an AdS/CFT interpretation is then possible. Building on this intuition we show that, at least in the static case, the replacement of the conformal factor can be implemented dynamically by means of an interpolating flow which we construct explicitly. Furthermore, we show that this flow can be understood as the effect of irrelevant perturbations from the point of view of the dual two-dimensional CFT, and we identify the quantum numbers of the operators responsible for the flow. This allows us to address quantitatively the validity of CFT computations for these asymptotically flat black holes and provides a framework to systematically compute corrections to the CFT results.