Heterotic string theory on non‐Kähler manifolds with H‐flux and Gaugino condensate

Abstract

We discuss compactifications of heterotic string theory to four dimensions in the presence of H-fluxes, which deform the geometry of the internal manifold, and a gaugino condensate which breaks supersymmetry. We focus on the compensation of the two effects in order to obtain vacua with zero cosmological constant and we comment on the effective superpotential describing these vacua.

DWSB in heterotic flux compactifications

“…Σ mnp dy m ∧ dy n ∧ dy p . As already pointed out in [2,3,61] the presence of a non-trivial Σ modifies the scalar potential of the compactification. Indeed, following the computations of section 3, we see that the potential (3.13) is modified to…”

In the realm of the geometric transitions

“…So far most of the examples presented in the literature were compact complex non-Kähler manifolds [30] [35]. We prove the consistency of these manifolds by verifying that they satisfy the torsional constraint [44] [36].…”

“…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 combination of fluxes and a gluino condensate has been considered in [35][42] where it was argued that the superpotential (6.4) becomes W het = (H + idJ + Σ) ∧ Ω, (6.5) 23 For a derivation of this see [32]. 24 In the examples that we studied in this paper the gauge group is broken to a smaller subgroup by Wilson lines.…”

“…This theory has been studied in great detail over the last few years [30][31][32] [33][34] [35]. The manifold obtained on the heterotic side is a non-Kähler manifold and the fluxes will appear as torsion [36].…”

Heterotic models without fivebranes

“…also [21], [22], [23]. The severe consistency problem stems from the fact that the non-trivial H-field (induced from a mismatch between trR ∧ R and trF ∧ F ) has actually to be used at the same time consistently on the right hand side of the anomaly balance for the connection ω + aH from which trR ∧ R is computed.…”