71,798 research outputs found
Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory
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 -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.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry
and references adde
Positive Ricci curvature on highly connected manifolds
For let be a -connected closed manifold. If
mod assume further that is -parallelisable. Then
there is a homotopy sphere such that admits a
Ricci positive metric. This follows from a new description of these manifolds
as the boundaries of explicit plumbings.Comment: Corrected some minor typos and changed document class to amsart. The
new document class added 10 pages, so the paper is now now 46 page
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