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Trivertices and a corresponding class of hyperKahler spaces

Presented by: 
A Hanany Imperial College London
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons