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Title:
Higgs Bundles for G2 Manifolds and Brane/Particle Probes
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Abstract:
We consider M-theory on a local, ALE-fibered G2 manifold. At low energies the effective physics is described by a partially twisted 7d SYM theory. The BPS equations describe a Higgs bundle associated to the ALE fibration of the G2 manifold. We describe how M2-branes probing the G2 manifold descend to particles probing the Higgs bundle. Such probe particles attach a Morse-Witten complex to the geometry. This complex is generated by the singular subloci of the G2 manifold. Supersymmetric three-spheres are in correspondence with flow trees and give rise to boundary maps and cup products.
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