BPS action and superpotential for heterotic string compactifications with fluxes

Abstract

We consider N = 1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O (α ′2 ) the associated action can be written as a sum of squares of BPS-like quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus stabilization for a class of examples.

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

“…The integrated fluxes can be described [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] as gaugings of the supergravity theory and, in this section, we derive the corresponding gauge algebra for a generic class of freely-acting (a)symmetric orbifolds. 1 In particular, we will not limit ourselves to orbifolds which are connected to symmetric ones by a chain of T-dualities, but rather consider quite generic cases which may lie in different conjugacy classes of the Tduality group, than the symmetric ones.…”

In the realm of the geometric transitions

“…As was discussed in [29], [34], one can minimize the superpotential (1.4) to determine the background torsional equation as:…”

“…The most generic superpotential for the type I theory is then [29], [34] Performing an S-duality to go from type I string to the heterotic string, the D5 branes become NS5 branes, the field H RR becomes H NS ≡ H and the compactification manifold remains non-Kähler. The superpotential therefore is [29], [34] W het = (H + idJ) ∧ Ω, (6.4) where H is the usual three-form of the heterotic theory satisfying dH = tr R∧R− What about the possibility of having a gluino condensate in the heterotic string as described in [73]?…”

“…The manifold obtained on the heterotic side is a non-Kähler manifold and the fluxes will appear as torsion [36]. In this theory the moduli stabilization is achieved via the new superpotential proposed in [29] (see also [34]) 4) where H is the heterotic three-form satisfying dH = tr R ∧ R − 1 30 tr F ∧ F .…”

Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra

“…The complex flux H (3) − ie 2φ d e −2φ J is required to be (2,1) and primitive. It has been argued that the (2,1) condition follows from an analogous superpotential [48,47,49], although this is more subtle than in the IIB case.…”