A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

And so we have a nontrivial embedding, which is in some sense diagonal between the two factors. That subgroup we are going to refer to as the '''tilted gauge group''', and now our field content, at least in the bosonic sector, is going to be a group manifold, an infinite-dimensional function space Lie group, but a group nonetheless. And we can now look at \(G / H_\tau\), and if we have any interesting representation of \(H\), we can form homogeneous vector bundles and work with induced representations. And that's what the fermions are going to be. So the fermions in our theory are going to be \(H\) modules, and the idea is that we're going to work with vector bundles of the form inhomogeneous gauge group producted over the tilted gauge group.