R^4 Corrections to D1D5p Black Hole Entropy from Entropy Function Formalism

TL;DR

This work confirms that Sen's entropy function formalism accurately yields the entropy of D1D5p black holes in type IIB string theory, even in the presence of intricate ten-dimensional Wald entropy expressions. It develops both a 5D reduction and a 10D near-horizon analysis to compute leading and alpha'-corrected entropies, showing that S_BH = 2π sqrt(N1 N5 Np) at leading order and obtaining a controlled correction from alpha'^3R^4 terms that remains independent of field-redefinition ambiguities. The results demonstrate the robustness of the entropy-function approach for higher-derivative corrected backgrounds and provide a practical route to quantify corrections in D1D5p systems. Overall, the paper broadens the applicability of the entropy function to complex string-theoretic backgrounds and clarifies how higher-derivative effects modify black hole entropy.

Abstract

We show that in IIB string theory and for D1D5p black holes in ten dimensions the method of entropy function works. Despite the more complicated Wald formula for the entropy of D1D5p black holes in ten dimensions, their entropy is given by entropy function at its extremum point. We use this method for computing the entropy of the system both at the level of supergravity and for its higher order alpha'^3R^4 corrections.