Heterotic solitons on four-manifolds
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| Format: | Preprint |
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2021
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| author | Moroianu, Andrei Murcia, Ángel Shahbazi, C. S. |
| author_facet | Moroianu, Andrei Murcia, Ángel Shahbazi, C. S. |
| contents | 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 $κ$ and consist of a Riemannian metric $g$, a metric connection with skew torsion $H$ on $TM$ and a closed one-form $φ$ on $M$ satisfying a differential system. In the limit $κ\to 0$, 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 $φ$, 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 $κ$ and yield, to the best of our knowledge, the first examples of Heterotic compactification backgrounds not locally isomorphic to supersymmetric compactification backgrounds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2101_10309 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Heterotic solitons on four-manifolds Moroianu, Andrei Murcia, Ángel Shahbazi, C. S. Differential Geometry High Energy Physics - Theory Primary: 53C20. Secondary: 53C21 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 $κ$ and consist of a Riemannian metric $g$, a metric connection with skew torsion $H$ on $TM$ and a closed one-form $φ$ on $M$ satisfying a differential system. In the limit $κ\to 0$, 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 $φ$, 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 $κ$ and yield, to the best of our knowledge, the first examples of Heterotic compactification backgrounds not locally isomorphic to supersymmetric compactification backgrounds. |
| title | Heterotic solitons on four-manifolds |
| topic | Differential Geometry High Energy Physics - Theory Primary: 53C20. Secondary: 53C21 |
| url | https://arxiv.org/abs/2101.10309 |