Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory

Details Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory

2008-03-17

arxiv.org/abs/0803.2260v2

Physics

High Energy Physics

High Energy Physics - Theory

40 Pages

Scientific paper

We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Omega-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlsson and Okounkov. In the last part of the paper we describe a way to obtain (q,t) identities using the refined topological vertex.

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