CHERN-SIMONS AND TWISTED SUPERSYMMETRY IN VARIOUS DIMENSIONS

We introduce special supersymmetric gauge theories in three, five, sev en and nine dimensions, whose compactification on two-, four-, six- an d eight-folds produces a supersymmetric quantum mechanics on moduli sp aces of holomorphic bundles and/or solutions to the analogues of insta nton equations in higher dimensions. The theories may occur on the wor ld-volumes of D-branes wrapping manifolds of a special holonomy, We al so discuss the theories with matter, (C) 1998 Elsevier Science B.V.