N=4 Topological Amplitudes and Black Hole Entropy

Abstract

We study the effects of N=4 topological string amplitudes on the entropy of black holes. We analyse the leading contribution associated to six-derivative terms and find one particular operator which can correct the entropy of N=4 black holes. This operator is BPS-like and appears in the effective action of type II string theory on K3 x T^2 or equivalently its heterotic dual on T^6. In both descriptions the leading contribution arises at one-loop, which we calculate explicitly on the heterotic side. We then consider whether this term has any consequences for the entropy of (large) N=4 black holes and find that it makes indeed a contribution at subleading order. Repeating the computation for small black holes with vanishing horizon area at the classical level, we prove that this coupling lifts certain flat directions in the entropy function thereby being responsible for the attractor equations of some moduli fields.

33 pages, references added, section 3.3 added

References in corpus (6)

• alpha'-Corrections to Extremal Dyonic Black Holes in Heterotic String Theory
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• N=4 Topological Amplitudes and String Effective Action
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• Topological Amplitudes and Physical Couplings in String Theory
• A New Class of N=2 Topological Amplitudes

Cited by in corpus (7)

• Holographic Quantum Critical Transport without Self-Duality
• Non-Abelian Tensor Towers and (2,0) Superconformal Theories
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Borcherds Algebras and N=4 Topological Amplitudes
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Generalized N=2 Topological Amplitudes and Holomorphic Anomaly Equation
• Automorphic Black Hole Entropy