The linear multiplet and ectoplasm

Abstract

In the framework of the superconformal tensor calculus for 4D N = 2 supergravity, locally supersymmetric actions are often constructed using the linear multiplet. We provide a superform formulation for the linear multiplet and derive the corresponding action functional using the ectoplasm method (also known as the superform approach to the construction of supersymmetric invariants). We propose a new locally supersymmetric action which makes use of a deformed linear multiplet. The novel feature of this multiplet is that it corresponds to the case of a gauged central charge using a one-form potential not annihilated by the central charge (unlike the standard N = 2 vector multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear vectortensor multiplet. As a byproduct of our construction, we also find a variant realization of the tensor multiplet in supergravity where one of the auxiliaries is replaced by the field strength of a gauge three-form.

Superforms in five-dimensional, N = 1 superspace

“…The component field content of this section also indicates a relation to the results of [28,40]. When one reduces the component field content of the 3-form Eĉdê to four dimensions, one obtains a 2-form gauge field E cd5 and a four-dimensional gauge 3-form E cde .…”

“…There are also other extensions to flat superspace that may be considered; 4D, N = 2 centrally-extended superspaces have been considered in [40,45] and have a close relationship with 5D, N = 1 given that the central charge can be considered a ∂ 5 term. Centrallyextended 5D superspace was investigated in [46] where the central charge was gauged and several superforms were constructed; their relationship to the forms presented here is also JHEP05(2015)049 of interest.…”

The anomalous current multiplet in 6D minimal supersymmetry

“…The linear multiplet can be described using a four-form gauge potential B = 17) where the gauge parameter ρ is an arbitrary three-form. 4 The corresponding field strength is…”

Superforms in six-dimensional superspace

“…JHEP05 (2016)016 with the integral taken over some 5-dimensional bosonic subspace N of M with normal vector n. The full analysis of the four-dimensional analogue of this was carried out in reference [6]. In section 4.6, we found that the correct Ansatz for the 6-form was L sssψψψ = s i γ ψψψ s j s γk L αijk .…”

“…6 When Φ is homogeneous of degree n in the variables v, Φ is said to have homogeneity weight n. When we wish to indicate this explicitly, we will do so with a superscript Φ +n . In these terms, equation (2.9) says that the pure spinor projection ω +n λ...λψ...ψ of the lowest-dimension, non-vanishing component of the p-form is an analytic superfield with homogeneity weight n. The dimension of this field is d =…”