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Compactifications of heterotic strings on non-Kähler complex manifolds. II. (English) Zbl 1097.81703
Summary: We continue our study of heterotic compactifications on non-Kähler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kähler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kähler complex manifolds with torsion in lower dimensions, that have nonzero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kähler manifolds and illustrate how some results well known for Calabi-Yau compactifications, including counting the number of generations, apply to the non-Kähler case. We briefly address various issues regarding possible phenomenological applications.
Part I, cf. K. Becker et al., J. High Energy Phys. 2003, No. 4, 007, 60 pp. (electronic) (2003)].

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32J81 Applications of compact analytic spaces to the sciences
81T50 Anomalies in quantum field theory
83E30 String and superstring theories in gravitational theory
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