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

TL;DR

This work analyzes Type IIB compactifications on Calabi–Yau threefolds with Calabi–Yau valued NS-NS and RR 3-form backgrounds, which charge the dilaton hypermultiplet and generate a nontrivial classical potential $V$ in $N=2$ supergravity. It derives a symplectic, prepotential-independent formula for the classical potential that accommodates both electric and magnetic charges and studies minima in the electric-only and general magnetically charged cases. The results show that, within perturbation theory, minima are generally not supersymmetric and are often not within the regime of validity; however, at conifold and Argyres–Douglas singularities there can be $N=2$ minima or flat directions, with a topology-changing transition of the Calabi–Yau. The analysis also notes a global $N=0$ vacuum at vanishing Calabi–Yau volume, highlighting the challenge of achieving stable supersymmetric vacua in this setup.

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.