Abstract
A necessary condition for partial breaking of mathcal{N} = 2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest of these deformations which already occurs in mathcal{N} = 1 global supersymmetry, and its coupling to supergravity. It can be viewed as an imaginary constant shift of the D-auxiliary real field of an abelian gauge multiplet. We show how this deformation describes the magnetic dual of a Fayet-Iliopoulos term, a result that remains valid in supergravity, using its new-minimal formulation. Local supersymmetry and the deformation induce a positive cosmological constant. Moreover, the deformed U(1) Maxwell theory coupled to supergravity describes upon elimination of the auxiliary fields the gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we construct the chiral spinor multiplet in superconformal tensor calculus by working out explicitly its transformation rules and use it for an alternative description of the new-minimal supergravity coupled to a U(1) multiplet. We also discuss the deformed Maxwell theory in curved superspace.
Highlights
We make a first step towards this investigation by studying a non-trivial supersymmetry deformation in a simpler context, namely at the level of N = 1
We have studied in this work a deformation in N = 1 supersymmetry transformations corresponding to a shift of the real D-auxiliary field of a Maxwell multiplet by an imaginary constant, modifying the associated supersymmetric Bianchi identity by an integration constant
The deformed theory is the electric-magnetic dual of a theory with a Fayet-Iliopoulos term with the deformation parameter mapped to its constant coefficient
Summary
We have introduced in global supersymmetry a deformation of super-Maxwell theory which is the magnetic dual of the standard, electric, Fayet-Iliopoulos term. We use a superconformal formulation, which is certainly appropriate to describe the super-Maxwell system, and, since the idea is to use the linear multiplet L of eq (2.2) as compensating multiplet, we use the new-minimal formulation of N = 1 supergravity [9, 10].7. The resulting new-minimal theory can be transformed (before Poincare gauge fixing) into the old-minimal one by a superconformal chiral-linear duality transformation [11]. The superconformal formulation of new-minimal N = 1 supergravity uses a real linear multiplet L as compensator [7, 8, 11]. Gauge-fixing superconformal symmetry will generate a deformation parameter 4ζκ−2 in the Poincare theory, completely analogous to 4ζ in the global case
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