Flavour from partially resolved singularities

Abstract

In this letter we study topological open string field theory on D-branes in a IIB background given by non compact CY geometries O(n) ⊕ O(−2 − n) on P 1 with a singular point at which an extra fiber sits. We wrap N D5-branes on P 1 and M effective D3-branes at singular points, which are actually D5-branes wrapped on a shrinking cycle. We calculate the holomorphic Chern-Simons partition function for the above models in a deformed complex structure and find that it reduces to multi-matrix models with flavour. These are the matrix models whose resolvents have been shown to satisfy the generalized Konishi anomaly equations with flavour. In the n = 0 case, corresponding to a partial resolution of the A 2 singularity, the quantum superpotential in the N = 1 unitary SYM with one adjoint and M fundamentals is obtained. The n = 1 case is also studied and shown to give rise to two-matrix models which for a particular set of couplings can be exactly solved. We explicitly show how to solve such a class of models by a quantum equation of motion technique.

Boundary correlation numbers in one matrix model

“…Note added: After completion of this work authors of [33] let us know that the same model arises in string theory on partially resolved singularities. where α = (−1) p+2 √ 2(p+1)!…”