Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry

TL;DR

This paper develops a systematic method to construct an N=2 superfield Born-Infeld action with partial N=4 supersymmetry breaking, extending previous results and suggesting its self-duality.

Contribution

It introduces an iterative approach to derive the complete N=2 Born-Infeld action with partially broken N=4 supersymmetry, including higher-order terms beyond previous work.

Findings

Derived the N=2 Born-Infeld action up to the 10th order.

Connected the new action with earlier 8th order results by Kuzenko and Theisen.

Indicates the full action is likely self-dual.

Abstract

We propose a systematic way of constructing $N=2, d=4$ superfield Born-Infeld action with a second nonlinearly realized N=2 supersymmetry. The latter, together with the manifest N=2 supersymmetry, form a central-charge extended $N=4, d=4$ supersymmetry. We embed the Goldstone-Maxwell N=2 multiplet into an infinite-dimensional off-shell supermultiplet of this N=4 supersymmetry and impose an infinite set of covariant constraints which eliminate all extra N=2 superfields through the Goldstone-Maxwell one. The Born-Infeld superfield Lagrangian density is one of these composite superfields. The constraints can be solved by iterations to any order in the fields. We present the sought N=2 Born-Infeld action up to the 10th order. It encompasses the action found earlier by Kuzenko and Theisen to the 8th order from a self-duality requirement. This is a strong indication that the complete N=2 Born-Infeld action with partially broken N=4 supersymmetry is also self-dual.