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Eirik Svanes: Lectures

May 13, 2024
TITLE: Heterotic distance conjectures and symplectic cohomology

ABSTRACT: Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the complex structure deformations (the Beltrami differential). Treated separately, for large fluxes, or alternatively at large distances in the background complex structure moduli space, these fields can be integrated out to obtain a new field theory in the remaining fields, which describe the complexified hermitian and gauge degrees of freedom. We investigate properties of this new holomorphic theory, and in particular connections to the swampland distance conjecture in the context of heterotic string theory. In particular, the quadratic action gives rise to an elliptic complex, similar to the symplectic cohomologies of Tseng and Yau, but where the Beltrami differential of the large complex structure modulus plays the role of the symplectic form.

Slides of Lecture

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.