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A large \(N\) duality via a geometric transition. (English) Zbl 0983.81050

Summary: We propose a large \(N\) dual of \(4\)d, \(N=1\) supersymmetric, SU\((N)\) Yang-Mills with adjoint field \(\Phi\) and arbitrary superpotential \(W(\Phi)\). The field theory is geometrically engineered via D-branes partially wrapped over certain cycles of a non-trivial Calabi-Yau geometry. The large \(N\), or low-energy, dual arises from a geometric transition of the Calabi-Yau, where the branes have disappeared and have been replaced by suitable fluxes. This duality yields highly non-trivial exact results for the gauge theory. The predictions indeed agree with expected results in cases where it is possible to use standard techniques for analyzing the strongly coupled, supersymmetric gauge theories. Moreover, the proposed large \(N\) dual provides a simpler and more unified approach for obtaining exact results for this class of supersymmetric gauge theories.

MSC:

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