Manifolds of G_2 Holonomy from N=4 Sigma Model

Details Manifolds of G_2 Holonomy from N=4 Sigma Model Manifolds of G_2 Holonomy from N=4 Sigma Model

2002-01-20

arxiv.org/abs/hep-th/0201155v2

J.Phys.A35:8903-8912,2002

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 14 pages. Some comments are added,typos fixed. One reference added [17]. Final version accepted for publication in the

Scientific paper

10.1088/0305-4470/35/42/302

Using two dimensional (2D) N=4 sigma model, with $U(1)^r$ gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build " toric" hyper-Kahler eight real dimensional manifolds X_8. Dividing by one toric geometry circle action of X_8 manifolds, we present examples describing quotients $X_7={X_8\over U(1)}$ of G_2 holonomy. In particular, for the A_r Cartan matrix, the quotient space is a cone on a $ {S^2}$ bundle over r intersecting $\bf WCP^2_{(1,2,1)}$ projective spaces according to the A_r Dynkin diagram.

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