New half supersymmetric solutions of the heterotic string

Abstract

We describe all supersymmetric solutions of the heterotic string which preserve 8 supersymmetries and show that are distinguished by the holonomy, $\mathrm{hol}(\hat{\nabla })$, of the connection, $\hat{\nabla }$, with skew-symmetric torsion. The $\mathrm{hol}(\hat{\nabla })\subseteq SU(2)$ solutions are principal bundles over a 4-dimensional hyper-Kähler manifold equipped with a anti-self-dual connection and fibre group $G$ which has Lie algebra, ${\mathfrak Lie} (G)=\bR^{5,1}$, $\mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)$ or ${\mathfrak{cw}}_6$. Some of the solutions have the interpretation as 5-branes wrapped on $G$ with transverse space any hyper-Kähler 4-dimensional manifold. We construct new solutions for ${\mathfrak Lie} (G)=\mathfrak{sl}(2,\bR)\oplus \mathfrak{su}(2)$ and show that are characterized by 3 integers and have continuous moduli. There is also a smooth family in this class with one asymptotic region and the dilaton is bounded everywhere on the spacetime. We also demonstrate that the worldvolume theory of the backgrounds with holonomy SU(2) can be understood in terms of gauged WZW models for which the gauge fields are composite. The ${\rm hol}(\hat\nabla) \subseteq\bR^8$ solutions are superpositions of fundamental strings and pp-waves in flat space, which may also include a null rotation. The $\mathrm{hol}(\hat{\nabla })=\{1\}$ heterotic string backgrounds which preserve 8 supersymmetries are Lorentzian group manifolds.

31 pages, minor corrections, analysis improved and more references added

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• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Heterotic Black Horizons
• (1,0) superconformal theories in six dimensions and Killing spinor equations
• Spinorial geometry and Killing spinor equations of 6-D supergravity
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Heterotic supersymmetric backgrounds with compact holonomy revisited
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Geometry and supersymmetry of heterotic warped flux AdS backgrounds
• On small black holes, KK monopoles and solitonic 5-branes
• Higher-derivative corrections to small black rings
• Brane solitons of (1,0) superconformal theories in six dimensions with hypermultiplets
• NS5-branes, holography and CFT deformations
• Spinorial geometry, horizons and superconformal symmetry in six dimensions