### Trivertices and a corresponding class of hyperKahler spaces

Hanany, A *(Imperial College London)*

Monday 11 April 2011, 16:30-17:30

Seminar Room 1, Newton Institute

#### Abstract

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 http://arXiv.org/pdf/1012.2119

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