Solitonic strings and BPS saturated dyonic black holes

Abstract

We consider a six-dimensional solitonic string solution described by a conformal chiral null model with nontrivial $N=4\mathrm{}$ superconformal transverse part. It can be interpreted as a five-dimensional dyonic solitonic string wound around a compact fifth dimension. The conformal model is regular with the short-distance ("throat") region equivalent to a Wess-Zumino-Witten (WZW) theory. At distances larger than the compactification scale the solitonic string reduces to a dyonic static spherically symmetric black hole of toroidally compactified heterotic string. The new four-dimensional solution is parametrized by five charges, saturates the Bogomol'nyi bound, and has a nontrivial dilaton-axion field and moduli fields of a two-torus. When acted on by combined $T$- and $S$-duality transformations it serves as a generating solution for all the static spherically symmetric Bogomol'nyi-Prasad-Sommerfield saturated configurations of the low-energy heterotic string theory compactified on a six-torus. Solutions with regular horizons have the global space-time structure of extreme Reissner-Nordström black holes with the non-zero thermodynamic entropy which depends only on conserved (quantized) charge vectors. The independence of the thermodynamic entropy on moduli and axion-dilaton couplings strongly suggests that it should have a microscopic interpretation as counting degeneracy of underlying string configurations. This interpretation is supported by arguments based on the corresponding six-dimensional conformal field theory. The expression for the level of the WZW theory describing the throat region implies a renormalization of the string tension by a product of magnetic charges, thus relating the entropy and the number of oscillations of the solitonic string in compact directions.