Photon and photino as Nambu-Goldstone zero modes in an emergent SUSY QED

Abstract

We argue that supersymmetry with its well known advantages, such as naturalness, grand unification and dark matter candidate seems to possess one more attractive feature: it may trigger, through its own spontaneous violation in the visible sector, a dynamical generation of gauge fields as massless Nambu-Goldstone modes during which physical Lorentz invariance itself is ultimately preserved. We consider the supersymmetric QED model extended by an arbitrary polynomial potential of massive vector superfield that breaks gauge invariance in the SUSY invariant phase. However, the requirement of vacuum stability in such class of models makes both supersymmetry and Lorentz invariance to become spontaneously broken. As a consequence, massless photino and photon appear as the corresponding Nambu-Goldstone zero modes in an emergent SUSY QED, and also a special gauge invariance is simultaneously generated. Due to this invariance all observable relativistically noninvariant effects appear to be completely cancelled out among themselves and physical Lorentz invariance is recovered. Nevertheless, such theories may have an inevitable observational evidence in terms of the goldstino-photino like state presented in the low-energy particle spectrum. Its study is of a special interest for this class of SUSY models that, apart from some indication of an emergence nature of QED and the Standard Model, may appreciably extend the scope of SUSY breaking physics being actively studied in recent years.