Deviations from the Area Law for Supersymmetric Black Holes

TL;DR

The paper analyzes how higher-derivative interactions modify black hole entropy in four-dimensional N=2 compactifications, showing that Wald's Noether-charge framework provides a general, robust definition of entropy beyond the area law. By integrating the Noether potential over the horizon and employing special-geometry data from the holomorphic Wilsonian action, the authors derive explicit entropy formulas that incorporate R^2-type corrections and relate them to electric/magnetic charges through stabilization equations. They demonstrate, with concrete string-theory examples, that these macroscopic results can precisely match microscopic state counts and discuss how non-holomorphic corrections restore duality invariance in broader settings. The work highlights the central role of holomorphy, stabilization, and duality in reconciling macroscopic and microscopic descriptions of supersymmetric black holes.

Abstract

We review modifications of the Bekenstein-Hawking area law for black hole entropy in the presence of higher-derivative interactions. In four-dimensional N=2 compactifications of string theory or M-theory these modifications are crucial for finding agreement between the macroscopic entropy obtained from supergravity and the microscopic entropy obtained by counting states in string or M-theory. Our discussion is based on the effective Wilsonian action, which in the context of N=2 supersymmetric theories is defined in terms of holomorphic quantities. At the end we briefly indicate how to incorporate non-holomorphic corrections.