Oscillator Level for Black Holes and Black Rings

TL;DR

This paper establishes a gravitational dual for the oscillator level in the CFT description of black holes, linking horizon and asymptotic momentum via a Komar integral, enhancing understanding of black hole entropy in string theory.

Contribution

It identifies a Komar integral that equates the oscillator level at the horizon with total momentum at infinity, bridging CFT and gravitational descriptions of black holes.

Findings

Komar integral equals oscillator level at the horizon

Komar integral equals total momentum at infinity

Provides gravitational dual of CFT oscillator level

Abstract

Microscopic calculations of the Bekenstein-Hawking entropy of supersymmetric black holes in string theory are typically based on the application to a dual 2D CFT of Cardy's formula, S=2\pi \sqrt{c q /6}, where `c' is the central charge and `q' is the oscillator level. In the CFT, q is non-trivially related to the total momentum. We identify a Komar integral that equals q when evaluated at the horizon, and the total momentum when evaluated at asymptotic infinity, thus providing a gravitational dual of the CFT result.