Supersymmetry Algebra in Super Yang-Mills Theories

TL;DR

This paper computes the supersymmetry algebra in six-dimensional super Yang-Mills theories, explores dimensional reduction to lower dimensions, and extends the algebra to include hyper multiplets and maximally supersymmetric cases.

Contribution

It provides a detailed calculation of superalgebras in various dimensions and includes fermionic boundary contributions, extending previous results to hyper multiplets and maximally supersymmetric theories.

Findings

Fermionic contributions are boundary terms in superalgebra

Superalgebras in 5D and 4D are derived via dimensional reduction

Extended superalgebras include hyper multiplets and maximally supersymmetric cases

Abstract

We compute supersymmetry algebra (superalgebra) in supersymmetric Yang-Mills theories (SYM) consisting of a vector multiplet including fermionic contribution in six dimensions. We show that the contribution of fermion is given by boundary terms. From six dimensional results we determine superalgebras of five and four dimensional SYM by dimensional reduction. In five dimensional superalgebra the Kaluza-Klein momentum and the instanton particle charge are not the same but algebraically indistinguishable. We also extend this calculation including a hyper multiplet and for maximally SYM. We derive extended supersymmetry algebras in these four dimensional SYM with the holomorphic coupling constant given in hep-th/9408099.