Massive Interacting Yang-Mills Multiplets Nine and Five Dimensions

Abstract

We present interacting massive N=1 vector multiplet (VM) in nine dimensions (9D). Due to the identically-vanishing mass-term m(\Bar\lambda \lambda ) \equiv 0 for (symplectic) pseudo-Majorana gaugino in 9D, we employ unconventional technique to give masses to fermions. In 9D, we consider the gauge group G for the VM (A_\mu{}^I, \lambda^I , \varphi^I) (I = 1, 2, \cdots, dim G), where G is the Yang-Mills gauge group, and the gaugino \lambda^I is a pseudo-Majorana spinor. We break G by shifting the scalar \varphi^I, so that the gaugino \lambda^I as well as its super-partner gauge boson A_\mu{}^I will get the same mass. The scalar \varphi^I plays the role of a Nambu-Goldstone boson absorbed into the longitudinal components of A_\mu{}^I$, making the latter massive as a super-Proca-Stueckelberg mechanism. We also show that a similar method can be also applied to N=2 VMs in 5D.