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Gianluca Zoccarato: Lectures

September 16, 2020 (jointly with Mirjam Cvetic)

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.

Slides of Lecture, Part I

Slides of Lecture, Part II