Abstract
We present an extended version of the so-called Jackiw–Pi (JP) model in three dimensions, and perform its supersymmetrization. Our field content has three multiplets: (i) Yang–Mills vector multiplet (AμI,λI), (ii) Parity-odd extra vector multiplet (BμI,χI), and (iii) Scalar multiplet (CI,ρI;fI). The bosonic fields in these multiplets are the same as the original JP-model, except for the auxiliary field fI which is new, while the fermions λI, χI and ρI are their super-partners. The basic difference from the original JP-model is the presence of the kinetic term for CI with its modified field-strength HμI≡DμCI+mBμI. The inclusion of the CI-kinetic term is to comply with the recently-developed tensor hierarchy formulation for supersymmetrization.
Highlights
Ever since the work of Deser-Jackiw-Templeton [1], three dimensional (3D) gauge theory has drawn considerable attention
In this Letter, we have accomplished the N = 1 off-shell supersymmetrization of the extended JP-model [2]. This necessitates the introduction of the kinetic term of the CI -field
There are two reasons for our introduction of the kinetic term of the CI -field: First, it is motivated by the recent development of tensor hierarchy formulation [14][15]
Summary
Ever since the work of Deser-Jackiw-Templeton [1], three dimensional (3D) gauge theory has drawn considerable attention. We note that the 4D formulation of non-Abelian tensor multiplet [15] has three multiplets: vector multiplet (AμI, λI), a tensor multiplet (BμνI, χI, φ) and a compensator vector multiplet (CμI, ρI) These are 4D multiplets, and their 3D analogs are respectively our present vector multiplet (VM) (AμI, λI), an extra vector multiplet (EVM) (BμI, χI) and the scalar multiplet (SM) (CI, ρI).3) The fact that the compensator vector multiplet (CμI, ρI) in 4D has its own kinetic term indicates the SM (CI, ρI) in 3D should have its own kinetic terms to accomplish its supersymmetrization, even though the original JP-model had no such a kinetic term for the CI -field [2]. Note here that these remaining terms vanish exactly due to the CI -field equation:
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