Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory

Details Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory

1999-03-05

arxiv.org/abs/hep-th/9903056v2

Adv.Theor.Math.Phys. 4 (2000) 747-790

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 4 figures; minor corrections, comments on toric geometry and references added

Scientific paper

The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group representation theory to Lie algebras as well as crepant resolutions of Gorenstein singularities. On the physics side, we have the graph-theoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the ADE type in two complex dimensions. An intricate web of inter-relations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.

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