Abstract
We propose generalised mathcal{N} = 1 superconformal higher-spin (SCHS) gauge multiplets of depth t, {Upsilon}_{alpha (n)overset{cdot }{alpha }(m)}^{(t)} , with n ≥ m ≥ 1. At the component level, for t > 2 they contain generalised conformal higher-spin (CHS) gauge fields with depths t − 1, t and t + 1. The supermultiplets with t = 1 and t = 2 include both ordinary and generalised CHS gauge fields. Super-Weyl and gauge invariant actions describing the dynamics of {Upsilon}_{alpha (n)overset{cdot }{alpha }(m)}^{(t)} on conformally-flat superspace backgrounds are then derived. For the case n = m = t = 1, corresponding to the maximal-depth conformal graviton supermultiplet, we extend this action to Bach-flat backgrounds. Models for superconformal non-gauge multiplets, which are expected to play an important role in the Bach-flat completions of the models for {Upsilon}_{alpha (n)overset{cdot }{alpha }(m)}^{(t)} , are also provided. Finally we show that, on Bach-flat backgrounds, requiring gauge and Weyl invariance does not always determine a model for a CHS field uniquely.
Highlights
Due to their low conformal weights and high derivative Lagrangians, conformal higher-spin (CHS) fields are notoriously difficult to work with
We propose generalised N = 1 superconformal higher-spin (SCHS) gauge multiplets of depth t, Υ(αt()n)α (m), with n ≥ m ≥ 1
It has been conjectured that lower-spin conformal fields are neccesary in ensuring gauge invariance of minimal depth CHS fields on Bach-flat backgrounds [10]
Summary
For n ≥ m > 0, such a multiplet is formulated in terms of a prepotential Ψα(n)α (m), and its conjugate for n = m, defined modulo the gauge transformation δξ,ηΨα(n)α (m) = ∇(α1 ξα2...αn)α (m) + ∇ ̄ (α 1 ηα(n)α 2...αm) ,. With unconstrained gauge parameters ξα(n−1)α (m) and ηα(n)α (m−1). For n > m = 0, the prepotential Ψα(n) is defined modulo the gauge transformation δξ,λΨα(n) = ∇(α1 ξα2...αn) + λα(n) ,. Superconformal gauge-invariant actions for the multiplets (2.1) were constructed in [11] in Minkowski superspace, while for arbitrary conformally flat backgrounds they were derived in [14]. Superconformal gauge-invariant actions for the multiplets (2.2) with n > 1 were derived in [16] for conformally flat backgrounds. We generalise these multiplets by increasing the number of spinor derivatives appearing in their gauge transformations
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