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arXiv · 1012.5912

Gauge theory in dimension $7$

Frederik Witt
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Abstract

We first review the notion of a $G_2$-manifold, defined in terms of a principal $G_2$ ("gauge") bundle over a $7$-dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative submanifolds and present their deformation theory. In particular, we elaborate on a deformation problem with coassociative boundary condition. Its space of infinitesimal deformations can be identified with the solution space of an elliptic equation whose index is given by a topological formula.

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Frederik Witt. 2010-12-29. Gauge theory in dimension $7$. https://doi.org/10.1063/1.3089202

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