Variant 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 µ I , λ I , C µνρ I ) and (ii) A compensator tensor multiplet (B µν I , χ I , ϕ I ). The index I is for the adjoint representation of a non-Abelian gauge group. The C µνρ I is originally an auxiliary field Hodge-dual to the conventional auxiliary field D I . The ϕ I and B µν I are compensator fields absorbed respectively into the longitudinal components of A µ I and C µνρ I which become massive. After the absorption, C µνρ 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 χ I acquires a Dirac mass shared with the gaugino λ I . As an independent confirmation, we give the superspace re-formulation of the component results.

N=1supersymmetric Proca–Stueckelberg mechanism for extra vector multiplet

“…The C μνρ I -field is Hodge-dual to the conventional auxiliary field D I . The 'dilaton' ϕ I (or B μν I ) is absorbed into the longitudinal component of A μ I (or C μνρ I ), making the latter massive [2]. Our compensation mechanism in [2] works even with C μνρ I in the adjoint representation.…”

“…The 'dilaton' ϕ I (or B μν I ) is absorbed into the longitudinal component of A μ I (or C μνρ I ), making the latter massive [2]. Our compensation mechanism in [2] works even with C μνρ I in the adjoint representation. In this present paper, we demonstrate yet another field content as a supersymmetric compensator system in which an extra vector in the adjoint representation absorbs a scalar.…”

“…Even though the original Higgs mechanism [7] has been established experimentally [8], the Proca-Stueckelberg-type compensator mechanism for massive gauge fields [3] is still an important theoretical alternative. In our recent paper [2], we presented a variant supersymmetric compensator mechanism, both in component and superspace [9], with a field content different from [4]. Our formulation in [2] differs also from [1], because the field content in [2] consists of two multiplets: Yang-Mills (YM) vector multiplet (VM) (A μ I , λ I , C μνρ I ), and the tensor multiplet (TM) (B μν I , χ I , ϕ I ).…”

“…In our recent paper [2], we presented a variant supersymmetric compensator mechanism, both in component and superspace [9], with a field content different from [4]. Our formulation in [2] differs also from [1], because the field content in [2] consists of two multiplets: Yang-Mills (YM) vector multiplet (VM) (A μ I , λ I , C μνρ I ), and the tensor multiplet (TM) (B μν I , χ I , ϕ I ). The C μνρ I -field is Hodge-dual to the conventional auxiliary field D I .…”

“…Recently, there have been considerable developments [1,2] in the supersymmetrization of the Proca-Stueckelberg compensator mechanism [3]. The supersymmetrization of non-Abelian compensator mechanism was first performed in late 1980s [4].…”