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Manifolds of G_2 Holonomy from N=4 Sigma Model

Adil Belhaj
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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 $X_7={X_8\over U(1)}$ 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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Adil Belhaj. 2002-10-01. Manifolds of G_2 Holonomy from N=4 Sigma Model. https://doi.org/10.1088/0305-4470%2F35%2F42%2F302

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