Branes and N = 2 theories in two dimensions Original Research Article

Type IIA brane configurations are used to construct N = 2 supersymmetric gauge theories in two dimensions. Using localization of chiral multiplets in ten-dimensional space-time, supersymmetric non-linear sigma models with target space such as CPn−1 and the Grassmann manifolds are studied in detail. The quantum properties of these models are realized in M-theory by taking the strong Type IIA coupling limit. The brane picture implies an equivalence between the parameter space of N = 2 supersymmetric theories in two dimensions and the moduli space of vacua of N = 2 supersymmetric gauge theories in four dimensions. Effects like level-rank duality are interpreted in the brane picture as continuation past infinite coupling. The BPS solitons of the CPn−1 model are identified as topological excitations of a membrane and their masses are computed. This provides the brane realization of higher rank tensor representations of the flavor group.