Type II Small Stringy Black Holes, Probe Branes and Higher Derivative Interactions

TL;DR

This paper explores the geometry and entropy of small stringy black holes using probe branes, conformal field theory, and higher derivative corrections, revealing conditions for supersymmetry and entropy calculations.

Contribution

It connects probe brane analysis with conformal symmetry in AdS3 models and investigates higher derivative corrections affecting black hole entropy.

Findings

Probe analysis indicates supersymmetry via no-force condition.

Conformal symmetry in AdS3 models reproduces no-force constraints.

Higher derivative corrections simplify equations but require all-order analysis for entropy.

Abstract

The near horizon geometry of a fundamental string wrapped around an S1 reduced to four dimensions is expected to be AdS2 x S2. A probe string analysis suggests a no-force condition indicating supersymmetry, which coincides with the condition that the AdS2 is embedded in AdS3. We therefore consider the bulk string theory in terms of a WZW model on AdS3 following recent proposals by Dabholkar et. al and Giveon et. al. We find that conformal symmetry of the model naturally leads to the no-force constraints obtained from the probes. Moreover, we are able to extract the values of the moduli that account for the value of the microscopic entropy. We also investigate higher derivative corrections of the form alpha'^3 R^4 + flux terms to the horizon, in the context of type IIB supergravity. Imposing the no-force condition from the probe analysis leads to a striking simplification of the equations of motion at this order in alpha'. However, we argue that the value of the entropy can only be determined by considering all orders in alpha'.