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Register a new userMagnetic Deformation of Super-Maxwell Theory in Supergravity
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A necessary condition for partial breaking of 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 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.
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We propose a superspace formulation for the Weyl multiplet of N=1 conformal supergravity in five dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The minimal supergravity multiplet, which was introduced by Howe in 1981, emerges if one couples the Weyl multiplet to an Abelian vector multiplet and then breaks the super-Weyl invariance by imposing the gauge condition W=1, with W the field strength of the vector multiplet. The geometry of superspace is shown to allow the existence of a large family of off-shell supermultiplets that possess uniquely determined super-Weyl transformation laws and can be used to describe supersymmetric matter. Many of these supermultiplets have not appeared within the superconformal tensor calculus. We formulate a manifestly locally supersymmetric and super-Weyl invariant action principle. In the super-Weyl gauge W=1, this action reduces to that constructed in arXiv:0712.3102. We also present a superspace formulation for the dilaton Weyl multiplet.
We consider a non-anticommutative N=2 superspace with an SU(2) singlet and Lorentz scalar deformation parameter, ${theta^{alpha i},theta^{beta j}}_star = -2iP e^{alphabeta}e^{ij}$. We exploit this unique feature of the N=2 case to construct a deformation of the non-Abelian super-Yang-Mills theory which preserves the full N=2 supersymmetry together with the SU(2) R symmetry and Lorentz invariance. The resulting action describes a kind of heterotic special geometry with antiholomorphic prepotential $bar f(barphi) = Tr (barphi^2 (1+Pbarphi)^{-2})$.
We have extended previous analysis of the bulk/brane supersymmetrizations involving non-zero brane mass terms of bulk fermions (gravitini) and twisting of boundary conditions. We have constructed new brane/bulk models that may be relevant for realistic model building. In particular, we have built a model with the Randall-Sundrum bosonic sector, orthogonal projection operators on the branes in the fermionic sector, and an unbroken N=1 supersymmetry. We have also constructed 5d super-bigravity with static vacuum and unbroken N=1 supersymmetry, which may be viewed as a deconstruction of 5d supergravity.
Candidate counterterms break Noether-Gaillard-Zumino E_{7(7)} current conservation in N=8 supergravity in four dimensions. Bossard and Nicolai proposed a scheme for deforming the subsector involving vector fields in a Lorentz covariant manner, so as to restore duality. They argued that there must exist an extension of this deformation to the full theory that preserves supersymmetry. We show that it is not possible to deform the maximal supergravity to restore E_{7(7)} duality, while maintaining both general covariance and N=8 supersymmetry, as was proposed. Deformation of N=8 supergravity requires higher spins and multiple gravitons, which presents a concrete obstacle to this proposal.
This is a sequel of our paper hep-th/0606125 in which we have studied the {cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {cal N}=4 theory, with a complex deformation parameter beta and in the planar limit. There we have addressed the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter beta. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.
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