Arbitrary Number Of Vector Research Articles

N = 2 supergravity in five dimensions revisited

We construct matter-coupled N = 2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector, tensor and hypermultiplets. By allowing off-diagonal vector–tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi–Yau manifolds with fluxes.

BPS equations in \U0001d4a9 = 2, D = 5 supergravity with hypermultiplets

With the general aim to classify BPS solutions in \U0001d4a9 = 2, D = 5 supergravities interacting with an arbitrary number of vector, tensor and hypermultiplets, here we begin considering the most general electrostatic, spherical-symmetric BPS solutions in the presence of hypermultiplet couplings. We discuss the properties of the BPS equations and the restrictions imposed by their integrability conditions.

General matter coupled , D=5 gauged supergravity

We give the full lagrangean and supersymmetry transformation rules for D=5, N=2 supergravity interacting with an arbitrary number of vector, tensor and hyper-multiplets, with gauging of the R-symmetry group SU(2)_R as well as a subgroup K of the isometries of the scalar manifold. Among the many possible applications, this theory provides the setting where a supersymmetric brane-world scenario could occur. We comment on the presence of AdS vacua and BPS solutions that would be relevant towards a supersymmetric smooth realization of the Randall-Sundrum "alternative to compactification". We also add some remarks on the connection between this most general 5D fully coupled supergravity model and type IIB theory on the T^{11} manifold.

N = 1, D = 6 supergravity: Duality and non-minimal couplings

Six-dimensional supergravity theories and their duality properties play a central role in the context of string duality and string compactifications. Lowering dimensions usually leads to an increasing complexity of theories; in this respect six dimensions seem to constitute an appropriate compromise between the physical four and the presumably more fundamental ten or eleven dimensions. In this paper we present a superspace formulation of N = l, D = 6 supergravity with one tensor multiplet and an arbitrary number of vector- and hypermultiplets, in which the bosonic abelian superforms of the theory, the dilaton, the abelian gauge fields and the two-form are replaced by their S-duals i.e. four-, three- and two-superforms respectively, in compatibility with supersymmetry. As usual this replacement interchanges Bianchi identities with equations of motion. This formulation holds in the presence of one tensor multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell multiplets if all couplings are minimal. We determine the consistency conditions for non-minimal couplings in N = 1, D = 6 supergravity, for which we present a particularly significant solution, namely the one associated with the Chem-SimonsLorentz three-form which entails the Green-Schwarz anomaly cancellation mechanism. In the case of non-minimal couplings it is found that the gauge fields and the two-form can still be dualized while the dilaton has to remain a zero-form.

Two General Representation Theorems for Arbitrary‐Order‐Tensor‐Valued Isotropic and Anisotropic Tensor Functions of Vectors and Second Order Tensors

AbstractIn this paper, it is shown that irreducible representations for r‐th‐order‐tensor‐valued isotropic or anisotropic tensor functions depending on an arbitrary number of vectors and second order tensors as variables may be formed by the union of irreducible representations for certain r‐th‐order‐tensor‐valued isotropic or anisotropic tensor functions merely depending on not more than three variables (for r ≧ 1) or four variables (for r = 0) and hence that the representation problem for the former may be reduced to that for the latter.

SPONTANEOUS SYMMETRY BREAKING IN N=2 SUPERGRAVITY WITH MATTER

New versions of the N=2 supergravity hidden sector have been constructed allowing for spontaneous symmetry breaking without a cosmological term and with two arbitrary scales—the partial super-Higgs effect in particular. On this basis, spontaneous symmetry breaking has been investigated in the models of N=2 supergravity with an arbitrary number of vector- and hypermultiplets. As has been shown, the possibility at achieving breaking without a cosmological term is connected with the presence of nilpotent combinations of compact and noncompact generators in an isometry group of a σ model.

On third order tensor-valued isotropic functions

Representation theorems for tensor-valued isotropic functions known until now are extended to enclose the third order ones; they consist in sets of tensorial functions, depending on an arbitrary number of vectors and second order tensors as variables, such that every other tensorial function of the same type can be expressed as a linear combination of the elements in the corresponding set, through scalar coefficients. Irreducibility of these sets is also proved in the sense that none of their proper subsets satisfies this property.