Manifolds of G_2 Holonomy from N=4 Sigma Model

Adil Belhaj

doi:10.1088/0305-4470/35/42/302

Manifolds of G_2 Holonomy from N=4 Sigma Model

High Energy Physics - Theory 2008-11-26 v2

Authors: 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.

Keywords

G2 holonomy N=4 sigma model hyper-Kahler toric geometry Dynkin diagram

Cite

@article{arxiv.hep-th/0201155,
  title  = {Manifolds of G_2 Holonomy from N=4 Sigma Model},
  author = {Adil Belhaj},
  journal= {arXiv preprint arXiv:hep-th/0201155},
  year   = {2008}
}

Comments

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)

Manifolds of G_2 Holonomy from N=4 Sigma Model

Abstract

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