University of Birmingham > Talks@bham > Algebra Seminar > Classifying superconformal field theories via chiral rings

Classifying superconformal field theories via chiral rings

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If you have a question about this talk, please contact David Craven.

Postgraduate seminar

I will introduce the main mathematical ideas behind conformal field theory, using the N=2 minimal models as a concrete example. We will see how the so-called ‘chiral rings’ arise from basic Lie algebra representation theory plus ideas from quantum field theory. Then we’ll use the chiral rings to classify a special class of N=2 minimal models (those with ‘space-time supersymmetry’) into the famous ADE pattern (as seen in finite subgroups of SU(2), surface quotient singularities, simple finite-dimensional simply-laced Lie algebras, simply-laced Dynkin diagrams, etc.) Finally I’ll present the chiral rings of the entire class of N=2 minimal models (even those without the extra supersymmetry) and leave as an open question the classification of these theories.

This talk is part of the Algebra Seminar series.

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