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Trivertices and a corresponding class of hyperKahler spaces

Monday 11th April 2011 - 16:30 to 17:30
INI Seminar Room 1
Given a graph with lines and 3-valent vertices, one can construct, using a simple dictionary, a Lagrangian that has N=2 supersymmetry in 3+1 dimensions. The vacuum moduli space of such a theory is well known to give moment map equations for a HyperKahler manifold.

We will discuss the class of hyperkahler manifolds which arise due to such a construction and present their special properties. The Hilbert Series of these spaces can be computed and turns out to be a function of the number of external legs and loops in the graph but not on its detailed structure. The corresponding SCFT consequence of this property indicates a crucial universality of many Lagrangians, all of which have the same dynamics.

The talk is based on
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons