He, Y. & Song, J. S. (2000). Of McKay correspondence, nonlinear sigma model and conformal field theory. Advances in Theoretical and Mathematical Physics, 4(4), pp. 747790.

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Abstract
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 graphtheoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$models and LandauGinzburg 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 interrelations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.
Item Type:  Article 

Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/817 
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