Leading-order actions of Goldstino fields

Abstract

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

Stripping a supermultiplet of all but one scalar: a microscopic view

“…Finally, let us note that, as expected for the case of a low energy Lagrangian of a single goldstino, it was shown explicitly in [6,9,8,14,15,16] that the corresponding Lagrangian is the Volkov-Akulov one up to non-trivial field redefinitions.…”

Minimal constrained supergravity

“…The scale of susy-breaking f was set to one in [12]. A different formulation is that of Samuel and Wess [20], where the goldstino γ is related to the one of Volkov-Akulov by a non-trivial field redefinition (which can be found in [21,22] for global supersymmetric theories) and transforms as…”

Recursion relations from soft theorems

“…One the other hand, the low-energy effective Lagragian of Goldstinos can be constructed by a nilpotent constraint of the chiral superfield [34]. One can prove that the Lagrangian from constraint can be transferred to the Akulove-Volkov Lagrangian after a field redefinition [35][36][37][38][39].…”