TL;DR
This paper explores how M-theory backgrounds with specific holonomy groups correspond to Type IIA string theory configurations involving D6-branes wrapping supersymmetric cycles, enabling exact gauge theory computations.
Contribution
It establishes a correspondence between M-theory spaces with various holonomy groups and Type IIA D-brane configurations, providing a geometric framework for exact gauge theory calculations.
Findings
M-theory on spaces with special holonomy describes D6-branes on supersymmetric cycles.
Examples include lifts to M-theory with Spin(7), SU(3), G_2, and SU(4) holonomy.
The geometry allows for precise gauge theory quantity computations.
Abstract
We show that M-theory on spaces with irreducible holonomy represent Type IIA backgrounds in which a collection of D6-branes wrap a supersymmetric cycle in a manifold with a holonomy group different from the one appearing in the M-theory description. For example, we show that D6-branes wrapping a supersymmetric four-cycle on a manifold with G_2 holonomy is described in eleven dimensions by M-theory on a space with Spin(7) holonomy. Examples of such Type IIA backgrounds which lift to M-theory on spaces with SU(3), G_2, SU(4) and Spin(7) holonomy are considered. The M-theory geometry can then be used to compute exact quantities of the gauge theory on the corresponding D-brane configuration.
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