On the component structure of Script N = 1 supersymmetric nonlinear electrodynamics

We analyze the component structure of models for 4D N = 1 supersymmetricnonlinear electrodynamics that enjoy invariance under continuous dualityrotations. The N = 1 supersymmetric Born-Infeld action is a member of thisfamily. Such dynamical systems have a more complicated structure, especially inthe presence of supergravity, as compared with well-studied effectivesupersymmetric theories containing at most two derivatives (including nonlinearKahler sigma-models). As a result, when deriving their canonically normalizedcomponent actions, it becomes impractical and cumbersome to follow thetraditional approach of (i) reducing to components; and then (ii) applying afield-dependent Weyl and local chiral transformation. It proves to be moreefficient to follow the Kugo-Uehara scheme which consists of (i) extending thesuperfield theory to a super-Weyl invariant system; and then (ii) applying aplain component reduction along with imposing a suitable super-Weyl gaugecondition. Here we implement this scheme to derive the bosonic action ofself-dual supersymmetric electrodynamics coupled to the dilaton-axion chiralmultiplet and a Kahler sigma-model. In the fermionic sector, the actioncontains higher derivative terms. In the globally supersymmetric case, anonlinear field redefinition is explicitly constructed which eliminates all thehigher derivative terms and brings the fermionic action to a one-parameterdeformation of the Akulov-Volkov action for the Goldstino. The Akulov-Volkovaction emerges, in particular, in the case of the N = 1 supersymmetricBorn-Infeld action.Comment: 0+27 pages, no figures; V2: appendix, references added; V3: typos in eq. (6.7) corrected; V4: references, comments added, appendix B rewritten, version to appear in JHEP; V5: typos in eqs. (5.12) and (7.1) correcte