Mario Garcia-Fernandez

Torsion-Free Generalized Connections and Heterotic Supergravity

This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the Ricci tensor of a generalized metric, inspired by the work of Coimbra, Strickland-Constable and Waldram.

Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy

Balanced metrics on twisted Higgs bundles

\mathrm {SU}(3)

Infinitesimal moduli for the Strominger system and generalized Killing spinors

SU(3) and solutions of the Strominger system.

Moduli of

In this paper we construct new solutions of the Kähler–Yang–Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact Riemann surface. The resulting equations, which we call gravitating vortex equations, describe abelian vortices on the Riemann surface with back reaction of the metric. As a particular case of these gravitating vortices on the Riemann sphere we find solutions of the Einstein–Bogomol’nyi equations, which physically correspond to Nielsen–Olesen cosmic strings in the Bogomol’nyi phase. We use this to provide a Geometric Invariant Theory interpretation of an existence result by Y. Yang for the Einstein–Bogomol’nyi equations, applying a criterion due to G. Székelyhidi.

G_2

A twisted Higgs bundle on a Kähler manifold X is a pair

Gravitating vortices and the Einstein--Bogomol'nyi equations

(E,\phi )