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Eirik Svanes: Lectures

September 9, 2018
TITLE: String Dualities and an Infinity of Associative Submanifolds

ABSTRACT: By applying the F-theory/heterotic/M-theory duality chain the non-perturbative superpotential in F-theory discovered by Donagi, Grassi and Witten was recently used to conjecture that a certain M-theory G_2-manifold contains an infinite number of associative sub-manifolds, i.e. three-cycles calibrated with respect to the G_2 three-form. The corresponding M-theory superpotential derives from Euclidean M2 branes wrapping these associatives. I will prove the existence of these associative three-cycles at a certain orbifold point of the G_2 manifold, and connect the corresponding F-theroy superpotential through the M-theory/IIA/IIB/F-theory duality chain.

Slides of Lecture

January 10, 2018
TITLE: On marginal deformations of heterotic G2 geometries

ABSTRACT: A seven dimensional supersymmetric heterotic string compactification is a G_2 structure manifold Y equipped with an instanton bundle V, for which the geometry and bundle satisfy several coupled differential constraints. Ignoring higher curvature corrections, this includes G_2 holonomy manifolds with instanton bundles, but can also be more generic. Recently, the infinitesimal moduli of such compactifications was derived and identified with the first cohomology of a particular differential complex. I will review this result, and proceed to re-derive it from the two-dimensional sigma model point of view, whose target space is the above mentioned heterotic G_2 geometry. In particular, I will identify the worldsheet BRST operator whose cohomology is isomorphic to the infinitesimal deformations of the G_2 geometry. I will explain new concepts as they are introduced, in an effort to make the talk accessible to non-experts.