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We generalize the results of Polchinski and Strassler regarding the N=1-preserving mass deformation of N=4 SU(N) SYM theories and its string theory dual to SO(N) and USp(2N) gauge groups. The string theory duals involve 5-branes wrapped on RP^2. In order to match with the field theory classification of vacua, the 3-brane charge carried by such 5-branes must be shifted by a half, and this follows from a conjectured generalization of results of Freed and Witten. Our results provide an elegant physical picture for the classification of classically massive vacua in the mass-deformed N=4 theories.

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