Nonlinear vector–tensor multiplets revisited

Abstract

We give an off-shell formulation of the N = 2 supersymmetric new nonlinear vector-tensor multiplet. Interactions arise in this model as a consequence of gauging the central charge of the supersymmetry algebra, which in contrast to previous models with local central charge is achieved without a coupling to a vector multiplet. Furthermore, we present a new action formula that follows from coupling the N = 2 linear multiplet to the vector-tensor multiplet.In their study of four-dimensional N = 2 supersymmetric vacua of heterotic string theory de Wit et al. [1] found that the dilaton and the antisymmetric tensor reside in an N = 2 vector-tensor multiplet. Although on-shell a vector-tensor (VT) multiplet is dual to an abelian vector multiplet, string theory may prefer the off-shell realization of the former. This is why possible interactions of the VT multiplet have been extensively studied in the last years. Among these, which include a variety of couplings to additional vector multiplets [2]-[9] and supergravity couplings [10], there are self-interactions. A self-interacting VT multiplet with nonlinear supersymmetry transformations had been constructed for the first time by Claus et al. in [2]. Only recently was it realized that there exists a second self-interacting version of the multiplet: in [11] we obtained what we shall call the new nonlinear vector-tensor (NLVT) multiplet in the following by gauging its central charge transformations. Promoting the global bosonic symmetry associated with the central charge of the VT multiplet to a local symmetry requires the presence of a vector potential, which in previous works was taken to sit in an additional abelian vector multiplet [2,3,8,9]. In [11] on the other hand it was shown that the VT multiplet's own vector field can serve as the necessary gauge connection, as well. The resulting new NLVT multiplet features nonpolynomial but local interactions. They were constructed by means of the Noether method as a deformation of the free action and its symmetries, with the supersymmetry algebra being realized only on-shell. In the present paper we derive an off-shell formulation of the new NLVT multiplet from a suitable set of constraints on the field strengths appearing in the N = 2 supersymmetry algebra with a gauged central charge. The Bianchi identities imply that as a consequence of these constraints all field strengths can be expressed in terms of a single real scalar 1

The linear multiplet and ectoplasm

“…In particular, a general harmonic superspace formalism for 4D N = 2 rigid supersymmetric theories with gauged central charge was developed in [28]. Furthermore, a remarkable construction was given by Theis [29,30]. He proposed a new nonlinear vector-tensor multiplet with the defining properly that the central charge is gauged using the vector field belonging to the multiplet (unlike the approach of [28] which used an off-shell vector multiplet to gauge the central charge).…”

Superform formulation for vector-tensor multiplets in conformal supergravity

“…The constraints of[25] differ by a constant shift in L 12. This issue will be further discussed in[30] 13.…”

On supersymmetric Chern-Simons-type theories in five dimensions

“…This requires the gauge potential V to be inert under the action of the central charge, ∆V = 0. However, it was shown in [51,52] that in 4D it is possible to gauge the central charge with a gauge connection that is not annihilated by the central charge. To the best of our knowledge, the possibility of gauging the central charge with a gauge connection that is no longer inert under the central charge has never been properly analyzed in 5D.…”