Notes on Supersymmetric Gauge Theories in Five and Six Dimensions

TL;DR

This paper reviews the conditions for consistent supersymmetric gauge theories in five and six dimensions, explores their interrelations, and discusses mechanisms to avoid Landau poles and the role of multiplet mixing during dimensional reduction.

Contribution

It provides a comprehensive survey of supersymmetric gauge theories in higher dimensions and insights into their dimensional relations and consistency conditions.

Findings

Seiberg's necessary conditions for 5D and 6D theories

Discussion on avoiding Landau poles in non-asymptotically free theories

Analysis of tensor and vector multiplet mixing in dimensional reduction

Abstract

We investigate consistency conditions for supersymmetric gauge theories in higher dimensions. First, we give a survey of Seiberg's necessary conditions for the existence of such theories with simple groups in five and six dimensions. We then make some comments on how theories in different dimensions are related. In particular, we discuss how the Landau pole can be avoided in theories that are not asymptotically free in four dimensions, and the mixing of tensor and vector multiplets in dimensional reduction from six dimensions.