On Supercurrent Superfields and Fayet-Iliopoulos Terms in N=1 Gauge Theories

TL;DR

This paper analyzes the supermultiplet structure of Noether currents in N=1 supersymmetric gauge theories, clarifies their invariance properties, and explores the impact of Fayet-Iliopoulos terms and R-symmetry on supergravity coupling.

Contribution

It introduces a natural supercurrent multiplet invariant under all local symmetries and details how to derive and improve various supercurrent structures, including in theories with Fayet-Iliopoulos terms.

Findings

The natural supercurrent multiplet corresponds to the S-multiplet of Komargodski and Seiberg.

Improvement transformations can produce the Ferrara-Zumino multiplet and the Callan-Coleman-Jackiw energy-momentum tensor.

The non-dynamical superfield S can become propagating when R-symmetry is broken, affecting supergravity coupling.

Abstract

We revisit the supermultiplet structure of Noether currents for N=1 supersymmetric gauge theories. Using superfield identities and the field equations we show how to derive a superfield equation for the divergences of the Noether currents in terms of the supercurrent and anomaly superfields containing 16_B+16_F components. We refer to this as the natural supercurrent structure as it is invariant under all local symmetries of the theory. It corresponds to the S-multiplet of Komargodski and Seiberg. We clarify the on/off-shell nature of the currents appearing in this multiplet and we study in detail the effect of specific improvement transformations leading to 1) a Ferrara-Zumino multiplet and to 2) a multiplet containing the new improved energy-momentum tensor of Callan, Coleman and Jackiw. Our methods also apply to supersymmetric gauge theories with a Fayet-Iliopoulos term. We construct the natural supercurrent multiplet for such a theory and show how to improve this to a formally gauge-invariant Ferrara-Zumino multiplet by introducing a non-dynamical chiral superfield S to ensure superfield gauge invariance. Finally we study the coupling of this theory to supergravity and show that S remains non-dynamical if the theory is R-symmetric and that S becomes propagating if the theory is not R-symmetric, leading to non-minimal 16_B+16_F supergravity.