Lovelock type gravity and small black holes in heterotic string theory

TL;DR

This work investigates small two-charge black holes in heterotic string theory across spacetime dimensions D≥4 by employing a Lovelock-type action with all extended Gauss–Bonnet densities to capture α′-corrections. Using a near-horizon AdS$_2$×S^{D−2} ansatz and Wald entropy, the authors show there is a unique, D-independent choice of couplings λ_m (with λ_m = 1/(4^{m−1} m!)) that yields the universal entropy $S=4\pi\sqrt{nw}$ for all D, matching the statistical entropy of half-BPS string states. They demonstrate this explicitly for D=4,5 (fixing λ₂=1/8) and D=6,7 (fixing λ₃=1/96), and extend the result to general D via a recursive coupling pattern, implying a broad robustness of the entropy result under higher-curvature corrections. The findings suggest a potential link between Lovelock-type gravity and the tree-level heterotic string action, offering insight into how higher-curvature terms encode microscopic string-state degeneracies, while acknowledging that a full supersymmetric embedding and a complete action description in all dimensions remain open problems.

Abstract

We analyze near horizon behavior of small D-dimensional 2-charge black holes by modifying tree level effective action of heterotic string with all extended Gauss-Bonnet densities. We show that there is a nontrivial and unique choice of parameters, independent of D, for which the black hole entropy in any dimension is given by 4π\sqrt{nw}, which is exactly the statistical entropy of 1/2-BPS states of heterotic string compactified on T^{9-D}\times S^1 with momentum n and winding w. This extends the results of Sen [JHEP 0507 (2005) 073] to all dimensions. We also show that our Lovelock type action belongs to the more general class of actions sharing the simmilar behaviour on the AdS_2\times S^{D-2} near horizon geometry.