S. Bellucci et al., Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry - art. no. 025014, PHYS REV D, 6402(2), 2001, pp. 5014
We propose a systematic way of constructing an 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, forms a central-cha
rge 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 whi
ch eliminate all extra N = 2 superfields through the Goldstone-Maxwell one.
The Born-Infeld superfield Lagrangian density is one of these composite su
perfields. 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 th
e complete N = 2 Born-Infeld action with partially broken N = 4 supersymmet
ry is also self-dual.