Heterotic String Theory on non-Kaehler Manifolds with H-Flux and Gaugino Condensate

TL;DR

The paper investigates heterotic string compactifications with $H$-flux and a gaugino condensate on non-Kähler, $SU(3)$-structure internal manifolds, aiming to realize Minkowski vacua through complementary balancing mechanisms. It develops a no-scale, BPS-like square structure for the ten-dimensional action including the gaugino condensate, deriving geometric constraints such as a complex internal manifold, $SU(3)$ holonomy for the $\nabla^-$ connection, and a closed gaugino condensate $\Sigma$, with $H$ decomposing into $(2,1)+(1,2)$ and $(3,0)+(0,3)$ components tied to $dJ$ and $\Sigma$, respectively. The authors propose a unified four-dimensional superpotential $W = \int (H + i dJ + \Sigma) \wedge \Omega$ and discuss a no-scale effective potential, including an expected non-perturbative contribution $W_{\rm eff} \sim c + e^{-S}$ from the gaugino sector, linking microscopic flux/condensate data to the four-dimensional cosmological constant. They also address subtleties in variations of the condensate term and how the framework compares to Calabi–Yau cases, highlighting the role of the dilaton and potential phenomenological implications for moduli stabilization in heterotic contexts.

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.