Manifolds of G 2 Holonomy from N = 4 Sigma Model

Using two dimensional (2D) N = 4 sigma model, with U(1) gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build ” toric” hyperKahler eight real dimensional manifolds X8. Dividing by one toric geometry circle action of X8 manifolds, we present examples describing quotients X7 = X8 U(1) of G2 holonomy. In particular, for the Ar Cartan matrix, the quotient space is a cone on a S 2 bundle over r intersecting WCP2(1,2,1) weighted projective spaces according to the Ar Dynkin diagram.