Moduli stabilisation in heterotic models with standard embedding

Abstract

In this note we analyse the issue of moduli stabilisation in 4d models obtained from heterotic string compactifications on manifolds with SU(3) structure with standard embedding. In order to deal with tractable models we first integrate out the massive fields. We argue that one can not only integrate out the moduli fields, but along the way one has to truncate also the corresponding matter fields. We show that the effective models obtained in this way do not have satisfactory solutions. We also look for stabilised vacua which take into account the presence of the matter fields. We argue that this also fails due to a no-go theorem for Minkowski vacua in the moduli sector which we prove in the end. The main ingredient for this no-go theorem is the constraint on the fluxes which comes from the Bianchi identity.

DWSB in heterotic flux compactifications

“…We have also shown that, in the limit of constant dilaton, 1 2 DWSB compactification manifolds M reduce to half-flat geometriesM , like the ones considered in [48][49][50][51] in order to describe the effective 4d physics of heterotic flux compactifications. However, the working assumption of [48][49][50][51] is that the half-flat manifoldM is a small deviation of a certain Calabi-Yau manifoldM CY , and soM andM CY share the same set of light fields.…”

“…Note also that W 1 constant implies that θ = θ 0 is constant, and so without loss of generality we can set it to zero. This implies that our 'smeared' compactification manifoldM satisfies Im W 1 = Im W 2 = W 4 = W 5 = 0, or in other words that in such smeared limit 1 2 DWSB heterotic vacua reduce to compactifications in half-flat manifolds, like those studied in [46,[48][49][50][51].…”

“…However, the working assumption of [48][49][50][51] is that the half-flat manifoldM is a small deviation of a certain Calabi-Yau manifoldM CY , and soM andM CY share the same set of light fields. As our explicit construction does not rely on such assumption, one can use it to check to what extent such Calabi-Yau-inspired truncation is justified.…”

Stabilizing all Kähler moduli in type IIB orientifolds

“…The issue of moduli stabilization also has important implications for supersymmetry breaking and the cosmological constant. Considerable progress has been made in the field of moduli stabilization within various corners of string theory, such as Type IIA [3,27,42,70,72], Type IIB [11, 36, 40, 41, 58, JHEP12(2010)056 60,64,65], Heterotic [13,29,38,55,67] and G 2 compactifications of M theory [2,[4][5][6]30]. The simplest recipe for moduli stabilization and constructing vacua with a small positive cosmological constant (de Sitter vacua) within Type IIB string theory was proposed by Kachru, Kallosh, Linde, and Trivedi [58] (KKLT).…”

Exploring $SU(3)$ structure moduli spaces with integrable $G_2$ structures

“…A simple class of such vacua, that will be studied in this paper, are half-BPS domain wall solutions in four dimensions, that preserve N = 1 2 supersymmetry. As has been shown recently [23], the N = 1 2 supersymmetry constraints put very mild restrictions on the intrinsic torsion; for the most general H-flux preserving the symmetry of the ansatz, almost all torsion components can be balanced by the appropriate flux (for studies with restricted flux, see [24][25][26][27] for a ten-dimensional perspective, and [28][29][30][31][32] for four-dimensional studies). This heterotic set-up can thus be used to study the properties of many different types of SU (3) structure manifolds.The scope of this paper is to use heterotic N = 1 2 domain wall solutions to explore the moduli space of different SU (3) structure manifolds.…”