Branes and Six Dimensional Supersymmetric Theories

TL;DR

This paper explores six-dimensional supersymmetric theories arising from various brane configurations, demonstrating anomaly cancellation, RG fixed points, and connections to string theories with new fixed points and global symmetries.

Contribution

It introduces new six-dimensional models from brane setups, generalizes known instanton theories, and uncovers novel fixed points with enhanced symmetries at strong coupling.

Findings

Demonstrated anomaly-free brane configurations leading to 6D supersymmetric theories.

Identified infinite models with non-trivial RG fixed points at strong coupling.

Discovered new fixed points with $E_n$ symmetries in the strong coupling limit.

Abstract

We consider configurations of six-branes, five-branes and eight-branes in various superstring backgrounds. These configurations give rise to $(0,1)$ supersymmetric theories in six dimensions. The condition for RR charge conservation of a brane configuration translates to the condition that the corresponding field theory is anomaly-free. Sets of infinitely many models with non-trivial RG fixed points at strong coupling are demonstrated. Some of them reproduce and generalise the world-volume theories of SO(32) and $E_8\times E_8$ small instantons. All the models are shown to be connected by smooth transitions. In particular, the small instanton transition for which a tensor multiplet is traded for 29 hypermultiplets is explicitly demonstrated. The particular limit in which these theories can be considered as six-dimensional string theories without gravity are discussed. New fixed points (string theories) associated with $E_n$ global symmetries are discovered by taking the strong string coupling limit.