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Max Hübner: Lectures

June 8, 2022
TITLE: Getting High on Gluing Orbifolds (Part II)

ABSTRACT: In this second talk we extend our discussion from global quotients to more general classes of non-compact orbifolds. In particular we consider M-theory on elliptically fibered Calabi-Yau threefolds with non-compact discriminant loci and G2-spaces constructed as D6 brane uplifts. These setups engineer 5d conformal matter theories, 5d gauge theories and QCD-like theories in 4d and in all these cases we determine the global structure of flavor symmetries and possible 2-groups from geometry. With these results we turn to compact geometries constructed via gluing from local geometries. The gluing couples the QFTs associated with individual local patches to each other and gravity, and as a consequence flavor symmetries are broken or gauged. We characterize both processes geometrically.

September 13, 2021
TITLE: Higgs Bundles for G2 Manifolds and Brane/Particle Probes

We consider M-theory on a local, ALE-fibered G2 manifold.  At low energies the effective physics is described by a partially twisted 7d SYM theory. The BPS equations describe a Higgs bundle associated to the ALE fibration of the G2 manifold. We describe how M2-branes probing the G2 manifold descend to particles probing the Higgs bundle. Such probe particles attach a Morse-Witten complex to the geometry. This complex is generated by the singular subloci of the G2 manifold. Supersymmetric three-spheres are in correspondence with flow trees and give rise to boundary maps and cup products. 

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