Half-BPS cosmic string in Script N = 2 supergravity in the presence of a dilaton

We construct new half-BPS cosmic string solutions in D=4 N=2 supergravitycompatible with a consistent truncation to N=1 supergravity where they describeD-term cosmic strings. The constant Fayet-Iliopoulos term in the N=1 D-term isnot put in by hand but is geometrically engineered by a gauging in the motherN=2 supergravity theory. The coupling of the N=2 vector multiplets ischaracterized by a cubic prepotential admitting an axion-dilaton field, acommon property of many compactifications of string theory. The axion-dilatonfield survives the truncation to N=1 supergravity. On the string configurationthe BPS equations constrain the dilaton to be an arbitrary constant. All thecosmic string solutions with different values of the dilaton have the sameenergy per unit length but different lenght scales.Comment: 52 pages; typos correcte