Vortex-strings in N=2 quiver X U(1) theories

We study half-BPS vortex-strings in four dimensional N=2 supersymmetric quiver theories with gauge group SU(N)^n X U(1). The matter content of the quiver can be represented by what we call a tetris diagram, which simplifies the analysis of the Higgs vacua and the corresponding strings. We classify the vacua of these theories in the presence of a Fayet-Iliopoulos term, and study strings above fully-Higgsed vacua. The strings are studied using classical zero modes analysis, supersymmetric localization and, in some cases, also S-duality. We analyze the conditions for bulk-string decoupling at low energies. When the conditions are satisfied, the low energy theory living on the string's worldsheet is some 2d N=(2,2) supersymmetric non-linear sigma model. We analyze the conditions for weak to weak 2d-4d map of parameters, and identify the worldsheet theory in all the cases where the map is weak to weak. For some SU(2) quivers, S-duality can be used to map weakly coupled worldsheet theories to strongly coupled ones. In these cases, we are able to identify the worldsheet theories also when the 2d-4d map of parameters is weak to strong.Comment: 61 pages, 10 figure

On the Codimension Sequence of G-Simple Algebras

In the 80's, Regev, using results of Formanek, Procesi and Razmyslov in invariant theory and Hilbert series', determined asymptotically the codimension sequence of mXm matrices over an algebraically closed field of characteristic zero. Inspired by Regev's ideas, we found that the asymptotics of $c_{n}^{G}(A)$, the G graded codimension sequence of a finite dimensional G simple algebra A, is equal to $\alpha n^{\frac{1-\dim(A_{e})}{2}}(\dim(A)^{n}$ (this was conjectured by E.Aljadeff, D.Haile and M. Natapov), where \alpha is not yet determined number. Moreover, in the case where A is the algebra of mXm matrices with an arbitrary elementary G-grading we also manged to calculate \alpha