DWSB in heterotic flux compactifications

TL;DR

<p>We extend the domain-wall supersymmetry breaking (DWSB) framework to heterotic flux compactifications on SU(3)-structure manifolds with H-flux, constructing a 4D effective potential that is a sum of squares and reveals a no-scale pattern when supersymmetry is broken by a missing domain-wall calibration. The analysis connects the 4D potential to 10D BPS-like conditions expressed through SU(3)-structure data (J, Ω) and torsion classes, and identifies explicit torsion-induced SUSY-breaking vacua with calculable gravitino masses tied to the torsion W1. We further develop NS5-brane calibration and bundle stability notions in this non-supersymmetric setting, and present explicit examples via elliptic (T^2) fibrations, including Minkowski and AdS4 solutions, both with and without a gaugino condensate. The paper also discusses extending the DWSB mechanism to AdS4 vacua with gaugino condensates and outlines potential implications for lifting moduli and constructing controlled non-supersymmetric landscapes in heterotic string theory.</p>

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 four-dimensional 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.