Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton

Abstract

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton which obey the three-form Bianchi identity with curvature term taken with respect to either the Levi-Civita, the (+)-connection or the Chern connection. Among them, all our solutions with respect to the (+)-connection on the compact nilmanifold $M_3$ satisfy the heterotic equations of motion.

LaTeX, 16 pp., no figures, new Theorem 1.1, references added

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• Non-Kähler Calabi-Yau manifolds
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• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry
• Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients
• The Fu-Yau equation with negative slope parameter
• Killing-Yano tensors and some applications
• A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System
• Heterotic compactifications on nearly Kähler manifolds
• Heterotic Non-Kahler Geometries via Polystable Bundles on Calabi-Yau Threefolds
• Canonical metrics on holomorphic Courant algebroids
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• Invariant solutions to the Strominger system and the heterotic equations of motion
• Double quiver gauge theory and nearly Kahler flux compactifications
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Heterotic Black Horizons
• Moduli Stabilising in Heterotic Nearly Kähler Compactifications
• The Anomaly flow over Riemann surfaces
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Supersymmetric AdS_3 solutions in Heterotic Supergravity
• Geometry and supersymmetry of heterotic warped flux AdS backgrounds
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• Balanced Hermitian metrics from SU(2)-structures
• Calabi-Yau Manifolds and SU(3) Structure
• On the geometry underlying supersymmetric flux vacua with intermediate SU(2) structure
• The Heterotic-Ricci flow and its three-dimensional solitons
• Special Lagrangian cycles and Calabi-Yau transitions
• The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds
• Homogeneous heterotic supergravity solutions with linear dilaton
• Instantons on conical half-flat 6-manifolds
• The Anomaly flow on nilmanifolds
• Balanced and Aeppli Parameters for the Heterotic Moduli
• Minkowski spacetime and non-Ricci-flat compactification in heterotic supergravity
• Curvatures of real connections on Hermitian manifolds