How Does a Fundamental String Stretch its Horizon?

TL;DR

This paper investigates the interpolation of black hole solutions in heterotic string theory with higher derivative corrections, analyzing the horizon's physical radius and quantum entropy contributions.

Contribution

It provides a detailed analysis of interpolating solutions considering higher derivative terms and explores the effects on the horizon's physical radius and entropy.

Findings

The horizon's physical radius approaches a finite value despite vanishing moduli.

Higher derivative corrections introduce subtleties in constructing interpolating solutions.

Quantum corrections to entropy involve ambiguities when compared to statistical entropy.

Abstract

It has recently been shown that if we take into account a class of higher derivative corrections to the effective action of heterotic string theory, the entropy of the black hole solution representing elementary string states correctly reproduces the statistical entropy computed from the degeneracy of elementary string states. So far the form of the solution has been analyzed at distance scales large and small compared to the string scale. We analyze the solution that interpolates between these two limits and point out a subtlety in constructing such a solution due to the presence of higher derivative terms in the effective action. We also study the T-duality transformation rules to relate the moduli fields of the effective field theory to the physical compactification radius in the presence of higher derivative corrections and use these results to find the physical radius of compactification near the horizon of the black hole. The radius approaches a finite value even though the corresponding modulus field vanishes. Finally we discuss the non-leading contribution to the black hole entropy due to space-time quantum corrections to the effective action and the ambiguity involved in comparing this result to the statistical entropy.