Compactifications of Type IIB Strings to Four Dimensions with Non-trivial Classical Potential

Abstract

Type IIB strings are compactified on a Calabi-Yau three-fold. When Calabi-Yau-valued expectation values are given to the NS-NS and RR three-form field strengths, the dilaton hypermultiplet becomes both electrically and magnetically charged. The resultant classical potential is calculated, and minima are found. At singular points in the moduli space, such as Argyres-Douglas points, supersymmetric minima are found. A formula for the classical potential in $N=2$ supergravity is given which holds in the presence of both electric and magnetic charges.