Complex linear superfields, Supercurrents and Supergravities

TL;DR

This paper derives supercurrent expressions for 4D, N=1 complex linear superfield theories, verifies their conservation, and explores their coupling to supergravity, including higher derivative examples.

Contribution

It provides explicit supercurrent formulas, conservation verification, and a method for coupling to supergravity based on a superfield X, with applications to higher derivative theories.

Findings

Supercurrent expressions satisfy conservation equations.

Method to select supergravity formulations via superfield X.

Application to higher derivative superfield theories.

Abstract

We present expressions for the supercurrents generated by a generic $4D,~\mathcal{N}=1$ theory of complex linear superfield $\Sigma$. We verify that these expressions satisfy the appropriate superspace conservation equations. Furthermore, we discuss the component projection in order to derive expressions for the energy-momentum tensor, the supersymmetry current and the R-symmetry current when available. In addition, we discuss aspects of the coupling of the theory to supergravity. Specifically, we present a straightforward method to select the appropriate formulations of supergravity that one must use in order to do the coupling. This procedure is controlled by a superfield X originating from the Super-Poincar\'{e} invariance of the theory. We apply these results to examples of theories with higher derivative terms.