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Alessandro Tomasiello (University of Milano-Bicocca)
2024-07-15  10:40 - 12:00
Room 202, Astronomy and Mathematics Building

Leture Note

I will give an overview of the relations between generalized geometry and theoretical physics.

We will begin with supersymmetric solutions of type II supergravity. When there is a four-dimensional external Minkowski space, the internal six-dimensional manifold is generalized Kähler or complex, depending on the amount of supercharges. The system is also related to the Hull–Strominger equations for the heterotic string.

When the external space is Anti-de Sitter, integrability is broken in a controlled fashion, easily formulated in terms of pure spinors. A generalization of the usual notion of calibrations is also available.

Imposing supersymmetry in other dimensions, both even and odd, provides several extensions of these results. This includes generalizations of G2 and Sasaki–Einstein geometries. Some simple cases can be classified completely.

The physical notion of duality also suggests augmenting the generalized tangent bundle with some form bundles. The structure group often becomes exceptional. Supersymmetry can now be reformulated in terms of holonomy for this bundle, or with novel analogues of a generalized complex structure.