Heterotic solitons on four-manifolds

Abstract

We investigate four-dimensional Heterotic solitons, defined as a particular class of solutions of the equations of motion of Heterotic supergravity on a four-manifold $M$. Heterotic solitons depend on a parameter $\kappa$ and consist of a Riemannian metric $g$, a metric connection with skew torsion $H$ on $TM$ and a closed one-form $\phi$ on $M$ satisfying a differential system. In the limit $\kappa \to 0$, Heterotic solitons reduce to a class of generalized Ricci solitons and can be considered as a higher-order curvature modification of the latter. If the torsion $H$ is equal to the Hodge dual of $\phi$, Heterotic solitons consist of either flat tori or closed Einstein-Weyl structures on manifolds of type $S^1\times S^3$ as introduced by P. Gauduchon. We prove that the moduli space of such closed Einstein-Weyl structures is isomorphic to the product of $\mathbb{R}$ with a certain finite quotient of the Cartan torus of the isometry group of the typical fiber of a natural fibration $M\to S^1$. We also consider the associated space of essential infinitesimal deformations, which we prove to be obstructed. More generally, we characterize several families of Heterotic solitons as suspensions of certain three-manifolds with prescribed constant principal Ricci curvatures, amongst which we find hyperbolic manifolds, manifolds covered by $\widetilde{\mathrm{Sl}}(2,\mathbb{R})$ and E$(1,1)$ or certain Sasakian three-manifolds. These solutions exhibit a topological dependence in the string slope parameter $\kappa$ and yield, to the best of our knowledge, the first examples of Heterotic compactification backgrounds not locally isomorphic to supersymmetric compactification backgrounds.

Typos corrected. References fixed and updated

References in corpus (5)

• Gauge theory for string algebroids
• The Gibbons-Hawking ansatz in generalized Kähler geometry
• Geometric Partial Differential Equations from Unified String Theories
• Geometric Flows for the Type IIA String
• The Heterotic-Ricci flow and its three-dimensional solitons