Leading-order actions of Goldstino fields

Haishan Liu; Hui Luo; Mingxing Luo; Liucheng Wang

doi:10.1140/epjc/s10052-011-1793-0

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2024 Impact factor 4.8

Particles and Fields

Eur. Phys. J. C (2011) 71: 1793
https://doi.org/10.1140/epjc/s10052-011-1793-0

Regular Article - Theoretical Physics

Leading-order actions of Goldstino fields

Haishan Liu, Hui Luo, Mingxing Luo and Liucheng Wang^*

Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, Zhejiang, 310027, P.R. China

^* e-mail: liuchengwang@zimp.zju.edu.cn

Received: 30 May 2011
Revised: 28 September 2011
Published online: 8 November 2011

Abstract

This paper starts with a self-contained discussion of the so-called Akulov–Volkov action $\mathcal{S}_{\mathrm{AV}}$ , which is traditionally taken to be the leading-order action of the Goldstino field. Explicit expressions for $\mathcal{S}_{\mathrm{AV}}$ and its chiral version $\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}}$ are presented. We then turn to the issue on how these actions are related to the leading-order action $\mathcal{S}_{\mathrm{NL}}$ proposed in the newly proposed constrained superfield formalism. We show that $\mathcal{S}_{\mathrm{NL}}$ may yield $\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}}$ or a totally different action $\mathcal{S}_{\mathrm{KS}}$ , depending on how the auxiliary field in the former is integrated out. However, $\mathcal{S}_{\mathrm{KS}}$ and $\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}}$ always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.