2D Black Hole and Holographic Renormalization Group

TL;DR

This paper explores the connection between large N renormalization group flows in matrix quantum mechanics and the geometry of 2D Euclidean black holes, revealing how RG fixed points relate to black hole metrics and holographic RG flows.

Contribution

It demonstrates how the RG flow equations in a modified matrix quantum mechanics correspond to the radial evolution of bulk scalar fields in 2D black hole geometries, linking RG fixed points to black hole metrics.

Findings

RG fixed points exhibit negative specific heat.

The rescaling equation yields the 2D Euclidean black hole metric.

Flow equations match bulk scalar radial evolution.

Abstract

In hep-th/0311177, the Large $N$ renormalization group (RG) flows of a modified matrix quantum mechanics on a circle, capable of capturing effects of nonsingets, were shown to have fixed points with negative specific heat. The corresponding rescaling equation of the compactified matter field with respect to the RG scale, identified with the Liouville direction, is used to extract the two dimensional Euclidean black hole metric at the new type of fixed points. Interpreting the large $N$ RG flows as flow velocities in holographic RG in two dimensions, the flow equation of the matter field around the black hole fixed point is shown to be of the same form as the radial evolution equation of the appropriate bulk scalar coupled to 2D black hole.