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

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'.