SU(3)-instantons and $G_2,Spin(7)$-heterotic string solitons

Abstract

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimensions 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in $G_2$ arises from our considerations and Hitchin's flow equations, which seems to be new. Compact examples of $SU(3),G_2$ and $Spin(7)$ instanton satisfying the anomaly cancellation conditions are presented.

LaTex, 22 pages, Corrected anomaly cancellation, final version to appear in Commun. Math. Phys

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• On the geometry of closed G2-structure
• Canonical metrics on holomorphic Courant algebroids
• Gauge-Gravity Dualities, Dipoles and New Non-Kahler Manifolds
• The infinitesimal moduli space of heterotic $G_2$ systems
• Almost Hermitian Structures with Parallel Torsion
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Supersymmetric AdS Backgrounds in String and M-theory
• G_2-structures with torsion from half-integrable nilmanifolds
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• A classification of the torsion tensors on almost contact manifolds with B-metric
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity
• Remarks on string solitons
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds
• SU(3)-structures on submanifolds of a Spin(7)-manifold
• Octonionic instantons in eight dimensions
• Moduli of $G_2$ structures and the Strominger system in dimension 7
• The heterotic G${}_2$ system with reducible characteristic holonomy
• G-structures and Superstrings from the Worldsheet
• Classification of BPS equations in higher dimensions
• The Torsion of Spinor Connections and Related Structures
• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion
• The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5
• Solitons and exotic instantons
• Families of solutions of the heterotic G${}_2$ system
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds