A Large N Duality via a Geometric Transition

TL;DR

This paper introduces a large N duality for 4d N=1 supersymmetric SU(N) Yang-Mills theories with superpotentials, achieved through a geometric transition in Calabi-Yau manifolds, leading to exact results and a unified analytical framework.

Contribution

It proposes a novel large N duality via geometric transition that simplifies the analysis of complex supersymmetric gauge theories with arbitrary superpotentials.

Findings

Exact results match known strong coupling behaviors.

Duality provides a unified approach for various superpotentials.

Predictions agree with standard techniques where applicable.

Abstract

We propose a large N dual of 4d, 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N, or low-energy, dual arises from a geometric transition of the Calabi-Yau, where the branes have disappeared and have been replaced by suitable fluxes.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.