Deviations from the Area Law for Supersymmetric Black Holes

TL;DR

This paper reviews how higher-derivative interactions modify the black hole entropy area law in supersymmetric theories, highlighting the importance of holomorphic and non-holomorphic corrections for matching microscopic and macroscopic entropy calculations.

Contribution

It provides a detailed analysis of the modifications to the Bekenstein-Hawking area law in N=2 supersymmetric compactifications, emphasizing the role of the effective Wilsonian action and holomorphic quantities.

Findings

Higher-derivative interactions alter the classical entropy formula.

Holomorphic quantities are central to the effective action in N=2 theories.

Inclusion of non-holomorphic corrections refines entropy calculations.

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.