DWSB in heterotic flux compactifications

Abstract

Abstract:We address the construction of non-supersymmetric vacua in heterotic compactifications with intrinsic torsion and background fluxes. In particular, we implement the approach of domain-wall supersymmetry breaking (DWSB) previously developed in the context of type II flux compactifications. This approach is based on considering backgrounds where probe NS5-branes wrapping internal three-cycles and showing up as fourdimensional domain-walls do not develop a BPS bound, while all the other BPS bounds characterizing the N = 1 supersymmetric compactifications are preserved at tree-level. Via a scalar potential analysis we provide the conditions for these backgrounds to solve the ten-dimensional equations of motion including order α ′ corrections. We also consider backgrounds where some of the NS5-domain-walls develop a BPS bound, show their relation to no-scale SUSY-breaking vacua and construct explicit examples via elliptic fibrations. Finally, we consider backgrounds with a non-trivial gaugino condensate and discuss their relation to supersymmetric and non-supersymmetric vacua in the present context.

Gaugino condensation and the cosmological constant

“…A closer inspection reveals that most of these solutions lie outside the realm of our analysis, relying on: threshold corrections to the gauge coupling [15,16], worldsheet instantons (discussed above) [10], or a combination of these [9,11], strong coupling effects [17][18][19][20], or other non-perturbative dynamics [21]. However, there appear to be a few puzzling exceptions [22][23][24][25], which are at odds with our findings, since they engineer AdS 4 solutions using a combination of H-flux, α ′ corrections and gaugino condensates. According to our analysis, these solutions should not be possible.…”

“…An equivalent version of this statement, in terms of the ten-dimensional fields φ and A, was derived in [8] (see also [24]). We provide a proof of this statement in the subsequent paragraph.…”

“…As explained in the introduction, most heterotic AdS 4 solutions rely on additional α ′ or g s effects. However, we were able to identify a few outlying examples, [22][23][24][25], which generate AdS 4 solutions using only the ingredients considered in this analysis: H-flux, bundles, perturbative α ′ corrections, and gaugino condensates. The are two likely resolutions to this tension: the first concerns the validity of an α ′ expansion in torsional solutions, and the second involves solving the heterotic Bianchi identity.…”

G-structures and domain walls in heterotic theories

“…Then, the Killing spinor equations are given by 29) where the Weyl spinor ζ parameterizes supersymmetry, D I W = W I + K I W and (σ µ ) = (1 2 , σ α ), with the Pauli matrices σ a . The covariant derivatives D µ is defined by 30) with the spin connection ω µ .…”

The leading quantum corrections to stringy Kähler potentials

“…9 First let us examine the heterotic string and imagine a superpotential W generated by non-perturbative physics and perhaps by background fluxes. Flux induced superpotentials in the heterotic string have been described largely using duality with type IIB backgrounds in [32][33][34][35]. These superpotential discussions are on a somewhat less secure footing than the type IIB case because the full space of chiral fields on which the superpotential and Kähler potential depend are not visible in supergravity.…”