Manifolds of Fixed Points and Duality in Supersymmetric Gauge Theories

TL;DR

This paper explores the structure of fixed points in four-dimensional superconformal gauge theories, revealing continuous families of infrared fixed points and connections between different dualities, supported by algebraic methods.

Contribution

It introduces a unified algebraic framework to understand fixed points and dualities in supersymmetric gauge theories, extending known examples and establishing new relations.

Findings

Existence of continuous families of IR fixed points in superconformal theories

Relation between Seiberg duality and duality in finite ${ m N}=2$ theories

Algebraic methods elucidate the structure of fixed points and dualities

Abstract

There are many physically interesting superconformal gauge theories in four dimensions. In this talk I discuss a common phenomenon in these theories: the existence of continuous families of infrared fixed points. Well-known examples include finite ${\cal N}=4$ and ${\cal N}=2$ supersymmetric theories; many finite ${\cal N}=1$ examples are known also. These theories are a subset of a much larger class, whose existence can easily be established and understood using the algebraic methods explained here. A relation between the ${\cal N}=1$ duality of Seiberg and duality in finite ${\cal N}=2$ theories is found using this approach, giving further evidence for the former. This talk is based on work with Robert Leigh (hep-th/9503121).