A Note on Six-Dimensional Gauge Theories

TL;DR

This paper explores six-dimensional gauge theories and their non-commutative versions, highlighting their role in string theory and M-theory, and examining the interplay of $ heta$-terms and non-commutative parameters.

Contribution

It introduces new six-dimensional gauge theories and analyzes their non-commutative generalizations within string theory frameworks, providing insights into their properties and Matrix descriptions.

Findings

$ heta$-term and non-commutative parameters are on equal footing.

These theories serve as Matrix descriptions of M-theory on $T^5$.

Applications to 5-branes in type IIB string theory.

Abstract

We study the new ``gauge'' theories in 5+1 dimensions, and their non-commutative generalizations. We argue that the $\theta$-term and the non-commutative torus parameters appear on an equal footing in the non-critical string theories which define the gauge theories. The use of these theories as a Matrix description of M-theory on $T^5$, as well as a closely related realization as 5-branes in type IIB string theory, proves useful in studying some of their properties.