N=1 Non-Abelian Tensor Multiplet in Four Dimensions

TL;DR

This paper develops an N=1 supersymmetric model in four dimensions featuring a non-Abelian tensor multiplet, a vector multiplet, and a compensator multiplet, all with propagating fields and consistent couplings, including superspace reformulation and supergravity coupling.

Contribution

It introduces a novel N=1 supersymmetric non-Abelian tensor multiplet system with propagating fields and consistent couplings, extending to arbitrary SO(N) representations and coupling to supergravity.

Findings

Constructed component Lagrangian with kinetic terms for all fields.

Provided superspace reformulation confirming system consistency.

Extended the model to arbitrary SO(N) representations and coupled to supergravity.

Abstract

We carry out the N=1 supersymmetrization of a physical non-Abelian tensor with non-trivial consistent couplings in four dimensions. Our system has three multiplets: (i) The usual non-Abelian vector multiplet (VM) (A_\mu{}^I, \lambda^I), (ii) A non-Abelian tensor multiplet (TM) (B_{\mu\nu}{}^I, \chi^I, \varphi^I), and (iii) A compensator vector multiplet (CVM) (C_\mu{}^I, \rho^I). All of these multiplets are in the adjoint representation of a non-Abelian group G. Unlike topological theory, all of our fields are propagating with kinetic terms. The C_\mu{}^I-field plays the role of a Stueckelberg compensator absorbed into the longitudinal component of B_{\mu\nu}{}^I. We give not only the component lagrangian, but also a corresponding superspace reformulation, reconfirming the total consistency of the system. The adjoint representation of the TM and CVM is further generalized to an arbitrary real representation of general SO(N) gauge group. We also couple the globally N=1 supersymmetric system to supergravity, as an additional non-trivial confirmation.