Kahler versus Non-Kahler Compactifications

Abstract

We review our present understanding of heterotic compactifications on non-Kahler complex manifolds with torsion. Most of these manifolds can be obtained by duality chasing a consistent F-theory compactification in the presence of fluxes. We show that the duality map generically leads to non-Kahler spaces on the heterotic side, although under some special conditions we recover Kahler compactifications. The dynamics of the heterotic theory is governed by a new superpotential and minimizing this superpotential reproduces all the torsional constraints. This superpotential also fixes most of the moduli, including the radial modulus. We discuss some new connections between Kahler and non-Kahler compactifications, including some phenomenological aspects of the latter compactifications.

14 pages, Harvmac, Some part based on talks given at the QTS3 conference, University of Cincinnati and SUSY '03 at the University of Arizona; v2: Typos corrected, reference added; v3: references updated and a few typos corrected. Final version to appear in the QTS3 proceedings

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• Heterotic String Compactifications on Half-flat Manifolds II
• Gauge-Gravity Dualities, Dipoles and New Non-Kahler Manifolds
• On The Warped Heterotic Axion
• Dipole-Deformed Bound States and Heterotic Kodaira Surfaces
• Towards a Dark Sector Model from String Theory
• Moduli Stabilisation in Heterotic Models with Standard Embedding
• Left-invariant Einstein metrics on $S^3\times S^3$
• What if string theory has a de Sitter excited state?
• Towards New Classes of Flux Compactifications
• Chiral Zeromodes on Vortex-type Intersecting Heterotic Five-branes