Abstract
We introduce special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the world-volumes of D-branes wrapping manifolds of a special holonomy. We also discuss the theories with matter.
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