Geometric Unification of Higgs Bundle Vacua
Abstract
Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of branes give rise to different low energy effective field theories. This has been heavily used in the study of Mtheory on local $G_2$ spaces and Ftheory on local elliptically fibered CalabiYau fourfolds. In this paper we show that the 3D $\mathcal{N} = 1$ effective field theory defined by Mtheory on a local $Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N} = 1$ M and Ftheory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of Mtheory on such local $Spin(7)$ spaces, and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing $Spin(7)$ spaces from generalized connected sums.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.13682
 Bibcode:
 2020arXiv200313682C
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Differential Geometry
 EPrint:
 63 pages, 5 figures