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 M-theory on local G 2 spaces and F-theory on local elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D N = 1 effective field theory defined by M-theory on a local Spin(7) space unifies the Higgs bundle data associated with 4D N = 1 M-and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory 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.

Geometric Approach to 3D Interfaces at Strong Coupling

“…Our analysis was inspired by string compactification considerations, though we have mainly focused on field-theory considerations. In a related development, M-theory on noncompact Spin(7) backgrounds can sometimes be interpreted as generating interpolating profiles between 4D M-and F-theory vacua [109]. It would be very interesting to study time-reversal invariant configurations engineered from this starting point.…”