- 6/8/2022: Getting High on Gluing Orbifolds (Part II)
- 9/9/2021: Zero modes of Higgs bundles on local Spin(7) manifolds
- 9/16/2020: Unification of Higgs Bundles
- 4/11/2019: M3-branes and T-branes in G2 Backgrounds
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 9, 2021
TITLE: Zero modes of Higgs bundles on local Spin(7) manifolds
ABSTRACT: We employ Higgs bundles to study the 3D N=1 field theories obtained from M-theory compactified on a local Spin(7) space given as a four-manifold M4 of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. We emphasize topologically robust quantities such as “parity” anomalies of the 3D field theory which descend from topological data of geometric reflections of the compactification. Furthermore, we provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators. The analysis also allows us to track the spectrum of extended objects and their transformations under higher-form symmetries.
In other better-understood geometric flows (e.g. Ricci flow and mean curvature flow) solitons have played a key role in understanding singularity formation and hence in understanding the long-time behaviour of these flows. Time permitting I will make some comparisons with known solitons in Ricci flow and Lagrangian mean curvature flow. This is joint work with Johannes Nordström and also in part with Rowan Juneman (both at Bath).
September 16, 2020 (jointly with Gianluca Zoccarato)
TITLE: Unification of Higgs Bundles
ABSTRACT: We introduce a program to study compactifications of M-/F-theory on spaces with G2 and Spin(7) holonomy, which results in N=1 supersymmetry in four- and three-dimensions, respectively, by studying the world-volume gauge dynamics of Higgs bundles, which are associated with higher co-dimension singularities of special holonomy spaces.
Specifically, we will consider solutions of M-theory on local geometries with Spin(7) holonomy. The local geometry is an ADE fibration over a four manifold which gives a compactification of 7d supersymmetric Yang-Mills theory on Spin(7) manifold. The configurations of this system are controlled by a Higgs bundle on the four manifold. This Higgs bundle, which we will call the Spin(7) system, has the remarkable property of unifying other known Higgs bundles. We will show how solutions of other known Higgs bundles fit in the Spin(7) system and show how it is possible to use the Spin(7) system to create interpolating solutions between different Higgs bundles.
April 11, 2019
TITLE: M3-branes and T-branes in G2 Backgrounds