Variant N= 1 Supersymmetric Non-Abelian Proca-Stueckelberg Formalism in Four Dimensions

Abstract

We present a new (variant) formulation of N=1 supersymmetric compensator mechanism for an arbitrary non-Abelian group in four dimensions. We call this `variant supersymmetric non-Abelian Proca-Stueckelberg formalism'. Our field content is economical, consisting only of the two multiplets: (i) A Non-Abelian vector multiplet (A_\mu{}^I, \lambda^I, C_{\mu\nu\rho}{}^I) and (ii) A compensator tensor multiplet (B_{\mu\nu}{}^I, \chi^I, \varphi^I). The index I is for the adjoint representation of a non-Abelian gauge group. The C_{\mu\nu\rho}{}^I is originally an auxiliary field Hodge-dual to the conventional auxiliary field D^I. The \varphi^I and B_{\mu\nu}{}^I are compensator fields absorbed respectively into the longitudinal components of A_\mu{}^I and C_{\mu\nu\rho}{}^I which become massive. After the absorption, C_{\mu\nu\rho}{}^I becomes no longer auxiliary, but starts propagating as a massive scalar field. We fix all non-trivial cubic interactions in the total lagrangian, and quadratic interactions in all field equations. The superpartner fermion \chi^I acquires a Dirac mass shared with the gaugino \lambda^I. As an independent confirmation, we give the superspace re-formulation of the component results.