String theory and the 4D/3D reduction of Seiberg duality. A Review

Abstract

We review the reduction of four-dimensional N=1 Seiberg duality to three dimensions focusing on the D brane engineering approach. We start with an overview of four-dimensional Seiberg duality for theories with various types of gauge groups and matter content both from a field-theoretic and a brane engineering point of view. Then we describe two families of N=2 three-dimensional dualities, namely Giveon-Kutasov-like and Aharony-like dualities. The last part of our discussion is devoted to the 4D/3D reduction of the dualities studied above. We discuss both the analysis at finite radius, crucial for preserving the duality in the dimensional reduction, and the zero-size limit that must be supported by a real mass flow and a Higgsing, which can differ case by case. We show that this mechanism is reproduced in the brane description by T-duality, supplying a unified picture for all the different cases. As a bonus we show that this analysis provides a brane description for Aharony-like dualities.

Section added on localization. To be published in Physics Reports

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Cited by in corpus (12)

• SUSY monopole potentials in 2+1 dimensions
• Abelianization and Sequential Confinement in $2+1$ dimensions
• Monopole Quivers and new 3D N=2 dualities
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• On 3d Seiberg-like Dualities with Two Adjoints
• Generalized Giveon-Kutasov duality
• Branes, partition functions and quadratic monopole superpotentials
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Deconstructing Defects
• Webs of 3d $\mathcal{N}=2$ dualities with D-type superpotentials
• Chiral dualities for SQCD${}_3$ with D-type superpotential
• On s-confinement in 3d $\mathcal{N}=2$ gauge theories with anti-symmetric tensors