Weak Coupling Chambers in N=2 BPS Quiver Theory

Using recent results on BPS quiver theory, we develop a group theoretical method to describe the quiver mutations encoding the quantum mechanical duality relating the spectra of distinct quivers. We illustrate the method by computing the BPS spectrum of the infinite weak chamber of some examples of N=2 supersymmetric gauge models without and with quark hypermultiplets.Comment: 17 pages, 1 figur

Refining the Shifted Topological Vertex

We study aspects of the refining and shifting properties of the 3d MacMahon function $\mathcal{C}_{3}(q)$ used in topological string theory and BKP hierarchy. We derive the explicit expressions of the shifted topological vertex $\mathcal{S}_{\lambda \mu \nu}(q)$ and its refined version $\mathcal{T}_{\lambda \mu \nu}(q,t)$. These vertices complete results in literature.Comment: Latex, 14 pages, 2 figures. To appear in Jour Math Phy