Of McKay correspondence, non-linear sigma-model and conformal field theory

Yang Hui He, Jun S. Song

Research output: Contribution to journalReview articlepeer-review


The ubiquitous A-D-E 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 σ-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the A-D-E 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.

Original languageEnglish (US)
Pages (from-to)747-789
Number of pages43
JournalAdvances in Theoretical and Mathematical Physics
Issue number4
StatePublished - Jul 2000
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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