Magnetic deformation of super-Maxwell theory in supergravity

A necessary condition for partial breaking of $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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.

Inflation via gravitino condensation in dynamically broken supergravity

Gravitino-condensate-induced inflation via the super-Higgs effect is a UV-motivated scenario for both inflating the early universe and breaking local supersymmetry dynamically, entirely independent of any coupling to external matter. As an added benefit, this also removes the (as of yet unobserved) massless Goldstino associated to global supersymmetry breaking from the particle spectrum. In this review, we detail the pertinent properties and outline previously hidden details of the various steps required in this context in order to make contact with current inflationary phenomenology. The class of models of SUGRA we use to exemplify our approach are minimal four-dimensional N = 1 supergravity and extensions thereof with broken conformal symmetry. Therein, the gravitino condensate itself can play the role of the inflation, however the requirement of slow-roll necessitates unnaturally large values of the wave function renormalization. Nevertheless, there is an alternative scenario that may provide Starobinsky-type inflation, occurring in the broken-SUGRA phase around the nontrivial minima of the gravitino-condensate effective potential. In this scenario higher curvature corrections to the effective action, crucial for the onset of an inflationary phase, arise as a result of integrating out massive quantum gravitino fields in the path integral. The latter scenario is compatible with Planck satellite phenomenology but not with BICEP2 data.

SUPERSYMMETRY AND DIMENSIONALITY IN THE SUPERSTRING THEORY

The realization of non-linear global supersymmetry in the superstring theory requires the quadratic fermionic Lagrangian [Formula: see text], defined from the D-dimensional, Minkowski-space energy–momentum tensor Tmn, to have the same form as the quadratic gravitational contribution [Formula: see text] to the superstring Lagrangian. Here, we prove that this condition is only satisfied for the heterotic string theory after reduction to D = 4, irrespective of whether the original source of [Formula: see text] in ten or twenty-six dimensions is the quadratic term [Formula: see text] or the quartic term [Formula: see text]. If [Formula: see text] derives from [Formula: see text], the solution is D = 4 (or the unphysical value D = 1), while if we suppose that D≠4 and [Formula: see text] dominates, we obtain the (singular) solution (D-2)3 = 0. The world sheet is also discussed. The bosonic string and type-II superstring, on the other hand, yield solutions for D which are complex, non-integral, or at the singular point D = 2, where the Einstein equations hold identically.