Publicación: The Heterotic-Ricci Flow and Its Three-Dimensional Solitons
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2024-03-09
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info:eu-repo/semantics/embargoedAccess
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Springer Nature
Resumen
We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter, for a complete Riemannian metric and a three-form H on a manifold M. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion H. When the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when and the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form H. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining, in particular, the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton and leave as open the construction of a Heterotic soliton with non-constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.
Descripción
La versión registrada de este artículo, publicado por primera vez en J Geom Anal 34, 122 (2024), está disponible en línea en el sitio web del editor: https://doi.org/10.1007/s12220-024-01570-4.
The registered version of this article, first published in J Geom Anal 34, 122 (2024), is available online at the publisher's website: https://doi.org/10.1007/s12220-024-01570-4.
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Palabras clave
Riemannian curvature flows, riemannian solitons, supergravity differential equations, renormalization group flows
Citación
Moroianu, A., Murcia, Á.J. & Shahbazi, C.S. The Heterotic-Ricci Flow and Its Three-Dimensional Solitons. J Geom Anal 34, 122 (2024). https://doi.org/10.1007/s12220-024-01570-4
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Facultades y escuelas::Facultad de Ciencias
Departamento
Matemáticas Fundamentales