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

We consider M-theory on compact spaces of G2 holonomy constructed as orbifolds of the form (CY × S1)/2 with fixed point set Σ on the CY. This describes = 1 SU(2) gauge theories with b1(Σ) chiral multiplets in the adjoint. For b1 = 0, it generalizes to compact manifolds the study of the phase transition from the non-abelian to the confining phase through geometrical S3 flops. For b1 = 1, the non-abelian and Coulomb phases are realized, where the latter arises by desingularization of the fixed point set, while an S2 × S1 flop occurs. In addition, an extremal transition between G2 spaces can take place at conifold points of the CY moduli space where unoriented membranes wrapped on 1 and 2 become massless.