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Branes and $$N=2$$ theories in two dimensions. (English) Zbl 1052.81625
Summary: 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 $$\mathbb{C} P^{n-1}$$ 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 $$\mathbb{C} P^{n-1}$$ 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.

MSC:
 81T60 Supersymmetric field theories in quantum mechanics 81T13 Yang-Mills and other gauge theories in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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