Two-charge small black hole entropy: String-loops and multi-strings

TL;DR

This paper calculates the entropy of two-charge small black holes in heterotic string theory, incorporating string loop corrections and multi-string states, and finds consistency between microscopic and macroscopic entropy calculations.

Contribution

It introduces string-loop corrections and multi-string states into the entropy analysis of small black holes, providing a more complete microscopic understanding.

Findings

Entropy formula includes string-loop corrections: \u221a{a q_1 q_2 + b q_1}

Microstate counting with multi-strings matches macroscopic entropy for large charges

Scaling behavior relates to AdS_3 central charge and superconformal quantum mechanics

Abstract

We investigate the inclusion of 10-dimensional string loop corrections to the entropy function of two-charge extremal small black holes of the heterotic string theory compactified on S^1 x T^5 and show that the entropy is given by \pi\sqrt{a q_1 q_2+b q_1} where q_1 and q_2 are the charges with q_1 >> q_2 >> 1 and a and b are constants. Incorporating certain multi-string states into the microstate counting, we show that the new statistical entropy is consistent with the macroscopic scaling for one and two units of momentum (winding) and large winding (momentum). We discuss our scaling from the point of view of related AdS_3 central charge and counting of chiral primaries in superconformal quantum mechanics as well.