Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices

TL;DR

This paper constructs and analyzes cubic interactions between a complex linear superfield and higher spin supermultiplets, revealing specific coupling patterns, supercurrent structures, and duality relations for various spins.

Contribution

It introduces the construction of higher spin supercurrents and supertrace multiplets for complex linear superfields, including minimal and dual formulations, and explores their component currents.

Findings

Cubic interactions only occur with supermultiplets of spins j=s+1 and j=s+1/2.

Existence of an alternative minimal supercurrent multiplet with vanishing supertrace.

Duality transformation links the complex linear and chiral theories, with coupling signs depending on spin parity.

Abstract

We continue the program of constructing cubic interactions between matter and higher spin supermultiplets. In this work we consider a complex linear superfield and we find that it can have cubic interactions only with supermultiplets with propagating spins $j=s+1$, $j=s+1/2$ for any non-negative integer $s$ (half-integer superspin supermultiplets). We construct the higher spin supercurrent and supertrace, these compose the canonical supercurrent multiplet which generates the cubic interactions. We also prove that for every $s$ there exist an alternative minimal supercurrent multiplet, with vanishing supertrace. Furthermore, we perform a duality transformation in order to make contact with the corresponding chiral theory. An interesting result is that the dual chiral theory has the same coupling constant with the complex linear theory only for odd values of $s$, whereas for even values of $s$ the coupling constants for the two theories have opposite signs. Additionally we explore the component structure of the supercurrent multiplet and derive the higher spin currents. We find two bosonic currents for spins $j=s$ and $j=s+1$ and one fermionic current for spin $j=s+1/2$.