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What exactly are the ADE type of (susy) gauge theories? What exactly do we mean, intuitively, by ADE singularities? What are their relation to brane constructions and do you have any references from where one could understand the basics?

I tried to read a little bit of today's paper by Vafa et al. but could not even get the introduction. I would appreciate any information.

This post imported from StackExchange Physics at 2015-02-21 12:39 (UTC), posted by SE-user Marion

ADE refers to the ADE classification, which

refers to simply-laced simple Dynkin diagrams and corresponding Lie algebra and Lie group.

refers to finite subgroups $\Gamma$ of $SU(2)$, which is related to orbifolds $M/\Gamma$, i.e. manifolds with singularities. See also elementary catastrophes.

An ADE gauge theory means that the gauge group is an ADE Lie group. See also e.g. this Phys.SE post.

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