Non-Abelian Conifold Transitions and N=4 Dualities in Three Dimensions

TL;DR

This paper explores how non-abelian Higgs mechanisms in four-dimensional N=2 theories are geometrically realized via Calabi-Yau transitions, leading to N=4 dualities in three dimensions through string theory symmetries.

Contribution

It demonstrates the geometric realization of non-abelian Higgs mechanisms and derives N=4 dualities in three dimensions using string theory T-duality, confirming a conjecture relating gauge systems to exceptional tensionless strings.

Findings

Dualities in 3D N=4 theories are perturbative string symmetries.

Dual of a gauge system exists but may lack a Lagrangian description.

Confirmed a conjecture relating gauge duals to exceptional tensionless strings.

Abstract

We show how Higgs mechanism for non-abelian N=2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau threefolds. We use this result and T-duality of a further compacitification on a circle to derive N=4, d=3 dual field theories. This reduces dualities for N=4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover we find that the dual of a gauge system always exists but may or may not correspond to a lagrangian system. In particular we verify a conjecture of Intriligator and Seiberg that an ordinary gauge system is dual to compactification of Exceptional tensionless string theory down to three dimensions.