[Paper Review] Strings, higher curvature corrections, and black holes

Thomas Mohaupt|ArXiv.org|Dec 5, 2005

Black Holes and Theoretical Physics2 references4 citations

TL;DR

This paper reviews the microscopic origin of black hole entropy in string theory, focusing on supersymmetric (BPS) black holes and higher curvature corrections. It demonstrates quantitative agreement between statistical entropy from counting string states and macroscopic entropy via Wald's formula, establishing a deep link between string partition functions and black hole thermodynamics in extremal regimes.

ABSTRACT

We review old and recent results on subleading contributions to black hole entropy in string theory.

Motivation & Objective

• To understand the microscopic origin of black hole entropy in string theory, particularly for supersymmetric (BPS) black holes.
• To investigate how higher curvature corrections in the low-energy effective action affect black hole entropy beyond the naive area law.
• To explore the connection between the string partition function and the black hole partition function in the context of supersymmetric black holes.
• To assess the validity of the area law and Wald's generalized entropy formula in string-theoretic black hole microstate counting.
• To examine the role of non-perturbative and non-holomorphic corrections in reconciling microscopic and macroscopic entropy.

Proposed method

• Uses string perturbation theory to compute the asymptotic number of string states at high excitation levels, yielding a statistical entropy scaling as √N.
• Applies the low-energy effective action of massless string modes to construct supersymmetric black hole solutions with given mass and charges.
• Compares the macroscopic entropy S_macro = A/4 (with A the horizon area) to the microscopic entropy S_micro = log N from counting BPS states.
• Incorporates higher curvature corrections via Wald's entropy formula, which generalizes the area law to include curvature invariants.
• Analyzes the relation between the black hole partition function and the topological string partition function, suggesting a wave function interpretation.
• Examines non-perturbative corrections using proposals from [31] and [66], particularly in the large charge limit.

Experimental results

Research questions

• RQ1 To what extent does the statistical entropy of BPS states in string theory agree with the macroscopic entropy of corresponding supersymmetric black holes?
• RQ2 How do higher curvature corrections in the effective action modify the entropy formula beyond the naive area law?
• RQ3 What is the precise relationship between the string partition function and the black hole partition function in the BPS regime?
• RQ4 How do non-perturbative and non-holomorphic corrections affect the agreement between microscopic and macroscopic entropy?
• RQ5 Is the observed agreement between S_micro and S_macro an exact or asymptotic statement in the large charge limit?

Key findings

• For BPS black holes, the microscopic entropy log N computed from counting string states agrees precisely with the macroscopic entropy S_macro = A/4, including higher curvature corrections via Wald's formula.
• The agreement holds not only for the leading-order area law but also for subleading corrections, indicating that Wald's generalized entropy formula correctly captures the quantum gravitational effects.
• The statistical entropy of highly excited string states scales as √N, while the black hole entropy scales as g_S²N, and equality between them occurs at the string-black hole transition point where g_S²√N ≈ 1.
• The partition function of extremal black holes is directly related to the topological string partition function, suggesting a wave function interpretation in a minisuperspace approximation.
• Non-perturbative corrections, particularly in the large charge limit, are essential for a complete match between microscopic and macroscopic entropy, and are linked to the non-holomorphic corrections in the topological string amplitude.
• The framework provides a benchmark for quantum gravity: a controlled semi-classical limit where Einstein-Hilbert gravity with higher derivative corrections emerges from string theory, and black hole entropy is microscopically accounted for.