Novel N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 higher-spin supercurrents

Abstract

We study cubic interactions of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 massless integer-spin gauge supermultiplets in harmonic superspace. We construct the complete class of abelian (s, s1, s2) cubic vertices with the minimal number of space-time derivatives. Such vertices exist only for s ≥ s1 + s2 and universally take the form of the gauge prepotential coupled to the conserved higher-spin supercurrent. For s1 ≠ s2, we find the novel complex principal supercurrent, whose real and imaginary parts generate the parity-invariant and the parity-breaking interactions, respectively. The supercurrents are constructed from gauge-invariant N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2 higher-spin Weyl supertensors associated with the spin-s1 and spin-s2 gauge multiplets. These supertensors are defined in terms of unconstrained higher-spin analytic prepotentials. We also derive the complete set of conserved component higher-spin currents associated with the (s, s1, s2) vertices, including both traceless currents and currents with the non-vanishing trace.