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

TL;DR

This review discusses how four-dimensional N=1 Seiberg duality reduces to three dimensions using brane engineering, highlighting the role of T-duality and real mass flows in the dimensional transition.

Contribution

It provides a unified brane-based framework for understanding the 4D/3D reduction of Seiberg duality and related 3D dualities, including Aharony-like cases.

Findings

T-duality reproduces the reduction mechanism in brane descriptions.

The analysis offers a brane perspective on Aharony-like dualities.

Finite radius analysis is crucial for duality preservation during reduction.

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.