A 6D nonabelian $(1,0)$ Theory

Abstract

We construct a 6D nonabelian ${\cal N}=(1,0)$ theory by coupling an ${\cal N}=(1,0)$ tensor multiplet to an ${\cal N}=(1, 0)$ hypermultiplet. While the ${\cal N}=(1, 0)$ tensor multiplet is in the adjoint representation of the gauge group, the hypermultiplet can be in the fundamental representation or any other representation. If the hypermultiplet is also in the adjoint representation of the gauge group, the supersymmetry is enhanced to ${\cal N}=(2, 0)$, and the theory is identical to the $(2,0)$ theory of Lambert and Papageorgakis (LP). Upon dimension reduction, the $(1,0)$ theory can be reduced to a general ${\cal N}=1$ supersymmetric Yang-Mills theory in 5D. We discuss briefly the possible applications of the theories to multi M5-branes.