M. Cvetic et Aa. Tseytlin, SOLITONIC STRINGS AND BPS SATURATED DYONIC BLACK-HOLES, Physical review. D. Particles and fields, 53(10), 1996, pp. 5619-5633
We consider a six-dimensional solitonic string solution described by a
conformal chiral null model with nontrivial N=4 superconformal transv
erse part. It can be interpreted as a five-dimensional dyonic solitoni
c string wound around a compact fifth dimension. The conformal model i
s regular with the short-distance (''throat'') region equivalent to a
Wess-Zumino-Witten (WZW) theory. At distances larger than the compacti
fication scale the solitonic string reduces to a dyonic static spheric
ally symmetric black hole of toroidally compactified heterotic string.
The new four-dimensional solution is parametrized by five charges, sa
turates the Bogomol'nyi bound, and has a nontrivial dilaton-axion fiel
d 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 th
e static spherically symmetric Bogomol'nyi-Prasad-Sommerfield saturate
d configurations of the low-energy heterotic string theory compactifie
d on a six-torus. Solutions with regular horizons have the global spac
e-time structure of extreme Reissner-Nordstrom black holes with the no
n-zero thermodynamic entropy which depends only on conserved (quantize
d) charge vectors. The independence of the thermodynamic entropy on mo
duli and axion-dilaton couplings strongly suggests that it should have
a microscopic interpretation as counting degeneracy of underlying str
ing configurations. This interpretation is supported by arguments base
d on the corresponding six-dimensional conformal field theory. The exp
ression for the level of the WZW theory describing the throat region i
mplies a renormalization of the string tension by a product of magneti
c charges, thus relating the entropy and the number of oscillations of
the solitonic string in compact directions.