Phases of supersymmetric gauge theories from M-theory on G(2) manifolds

We consider M-theory on compact spaces of G(2) holonomy constructed as orbi folds of the form (CY x S-1)/Z(2) with fixed point set Sigma on the CY. Thi s describes N = 1 SU(2) gauge theories with b(1)(Sigma) chiral multiplets i n the adjoint. For b(1) = 0, it generalizes to compact manifolds the study of the phase transition from the non-abelian to the confining phase through geometrical S-3 flops. For b(1) = 1,the non-abelian and Coulomb phases are realized, where the latter arises by desingularization of the fixed point set, while an S-2 x S-1 flop occurs. In addition, an extremal transition be tween G(2) spaces can take place at conifold points of the CY moduli space where unoriented membranes wrapped on CP1 and RP2 become massless.