What is the connection between spin networks and ABJM's dual conformal symmetry?

[atyy]

This fascinating question was asked by our favourite blogger at http://physics.stackexchange.com/questions/5517/dual-conformal-symmetry-and-spin-networks-in-abjm .

 

[Physics Monkey]

It is an interesting question. The bare Chern-Simons part of the action definitely has a "spin network" description of some type. In condensed matter language there is a string net model that captures the topological physics of the doubled Chern-Simons $$SU(N)_k \times SU(N)_{-k}$$ theory. On the other hand, supersymmetry is pretty unnatural from the condensed matter point of view.