# Sylvester Gates, SUSY, Topology, Chern-Simons Theory

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Topic: ectoplasm conjecture.
Use pure group theory to study supersymmetry and supergravity.
M-theory and supergravity: 11 dimensions.
Superspace: interior of a sphere, ordinary space is an equatorial plane.
Consider the weight lattice for $\liesu_3$.
Define an action functional using $\stardstar$.
See nonlinear sigma model for pions?
See super curvature.
Covariant derivative allows coupling to matter fields.
See potential of a connection?
Given degrees of freedom, how are they represented?
Scalars? $n\dash$forms?
What are the representations of $\lieso_4$?
Which ones are spinor representations?
Traceless symmetric tensors correspond to gravitons?
Link between Young tableaux and Dynkin labels?
There are multiplication rules for both of these.
Can replace data of super fields with a poset of Young tableaux, stratified by level, and even just track them in a formal polynomial.
Group theory for physicists: representation theory of of compact Lie groups!
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