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 $\mathcal{N} = 1$ effective field theory defined by M-theory on a local $Spin(7)$ space unifies the Higgs bundle data associated with 4D $\mathcal{N} = 1$ 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.
Highlights
One of the very promising features of string theory is that it contains all of the qualitative ingredients necessary to couple the Standard Model of particle physics to quantum gravity
In this paper we show that the 3D N 1⁄4 1 effective field theory defined by M-theory on a local spin(7) space unifies the Higgs bundle data associated with 4D N 1⁄4 1 M- and F-theory vacua
In the previous sections we have shown that there is a natural interpretation of the local spin(7) equations as specifying an interpolating profile for Higgs bundle vacua obtained from the Pantev and Wijnholt (PW) and BHV systems
Summary
One of the very promising features of string theory is that it contains all of the qualitative ingredients necessary to couple the Standard Model of particle physics to quantum gravity. We show that if the four-manifold has an asymptotic region in which it is well approximated by a Kähler surface, the four-dimensional gauge theory reduces to that used in the study of 4D F-theory models [4,5,10,11] which we will refer to as the “BHV system.” In each of these specializations, some of the fields of the local spin(7) system asymptotically approach zero. In the M-theory region of the compactification, there is a local spacetime coordinate on a line RM-th which becomes part of the internal compactification geometry in the local BHV system Viewed in this way, the gluing region specified by the ambient G2 space for the local spin(7) Higgs bundle amounts to a gauge theoretic generalization of the twisted connected sum construction, in which various S1 factors have been decompactified. Some additional technical details on the analysis of solutions to the local spin(7) equations are presented in the Appendix
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