Manifolds of G_2 Holonomy from N=4 Sigma Model

Abstract

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 $X_7=\frac{X_8}{U(1)}$ 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 $\mathbf{WC}{\mathbf{P}}_{(1,2,1)}^2$ projective spaces according to the A_r Dynkin diagram.

Latex, 14 pages. Some comments are added,typos fixed. One reference added [17]. Final version accepted for publication in the J. Phys.A: Math.Gen.35(2002)

References in corpus (1)

• Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications

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