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Max Hübner: Lectures

September 13, 2022
TITLE: Generalized Symmetries and Compact Models

ABSTRACT: When coupling quantum field theories (QFTs) to each other and gravity their symmetries are believed to be gauged or broken. We consider this process for supersymmetric QFTs engineered in M-theory by local geometries of special holonomy and characterize the breaking and gauging of their higher symmetries. Here, the coupling of theories is geometrized by the embedding of local models into one compact model where topological data of the embedding determines the fate of n-form and n-group symmetries. With local and global K3 surfaces we take our starting point in 7d. We analyze the global structure of the resulting supergravity gauge group, generalizing and simplifying methods centered on Mordell-Weil groups for elliptic K3s, and give results for torus orbifolds. Next, we consider Calabi-Yau threefolds geometrizing couplings between localized 5d supersymmetric conformal sectors and determine the fate of their generalized symmetries.

September 9, 2022
TITLE: Higher Symmetries via Cutting and Gluing of Orbifolds

ABSTRACT: We study the higher symmetry structures of 4d, 5d, 7d quantum field theories (QFTs) which are geometrically engineered in M-theory by non-compact geometries with non-compact ADE loci. We characterize flavor and gauge Wilson lines of such QFTs via orbifold homology groups of the asymptotic boundary geometry and argue that the corresponding 0-form, 1-form and 2-group symmetries are mapped onto the Mayer-Vietoris sequence with respect to a covering derived from the asymptotic orbifold locus and its complement. Further, applying related cutting and gluing constructions to various compact geometries with ADE loci we discuss the global structure of the engineered supergravity gauge group.

Slides of Lecture

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.

Slides of Lecture

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

ABSTRACT:
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. 

Slides of Lecture