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.

Soft supersymmetry breaking in Calabi–Yau orientifolds with D-branes and fluxes

“…The equation of motion for dUα and dD α (2) coincides with the constraints obtained from the self-duality condition for F (5) . Eliminating dUα and dD α (2) from the action and one obtains the action (2.9) for the coordinates (2.10) and the Kähler potential (2.12).…”

“…For Calabi-Yau compactifications of type IIB theories this effective theory was determined in refs. [5,20,21,22] while for Calabi-Yau orientifolds it can be found in refs. [11,18,19,23].…”

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

“…In other words, it is flux which has support at infinity. While this flux is not directly piercing the compact cycles we show that, once appropriately regularized, it does introduce an effective superpotential for the complex structure moduli, which is generalization of the usual Gukov-Vafa-Witten superpotential [27,28,29] to 3-form flux with noncompact support. This is a way to introduce a general superpotential in a geometrically engineered N = 2 gauge theory.…”

BPS action and superpotential for heterotic string compactifications with fluxes

“…The derivation of this locking condition depended once more on the peculiar structure of the supersymmetry transformations to lowest order in α ′ , with the same type of structure entering in the gravitino and dilatino rules. The only relation which will remain valid in the presence of higher order α ′ corrections is the identification of the Nijenhuis tensor with the (3, 0) + (0, 3) parts of the torsion tensor, For a totally antisymmetric torsion tensor it also follows that 4) and R = R − T abc T abc .…”