Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions

We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.Comment: 47 pages; latex fil

The R-map and the Coupling of N=2 Tensor Multiplets in 5 and 4 Dimensions

We study the dimensional reduction of five dimensional N=2 Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor multiplets. The resulting 4D theories involve first order interactions among tensor and vector fields with mass terms. If the 5D gauge group, K, does not mix the 5D tensor and vector fields, the 4D tensor fields can be integrated out in favor of 4D vector fields and the resulting theory is dual to a standard 4D YMESGT. The gauge group has a block diagonal symplectic embedding and is a semi-direct product of the 5D gauge group K with a Heisenberg group of dimension (2P+1), where 2P is the number of tensor fields in five dimensions. There exists an infinite family of theories, thus obtained, whose gauge groups are pp-wave contractions of the simple noncompact groups of type SO*(2M). If, on the other hand, the 5D gauge group does mix the 5D tensor and vector fields, the resulting 4D theory is dual to a 4D YMESGT whose gauge group does, in general,NOT have a block diagonal symplectic embedding and involves additional topological terms. The scalar potentials of the dimensionally reduced theories naturally have some of the ingredients that were found necessary for stable de Sitter ground states. We comment on the relation between the known 5D and 4D, N=2 supergravities with stable de Sitter ground states.Comment: 42 pages;latex fil

A spinor approach to Walker geometry

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a certain constraint. Spinors therefore provide a natural tool for studying Walker geometry, which we exploit to draw together several themes in recent explicit studies of Walker geometry and in other work of Dunajski (2002) and Plebanski (1975) in which Walker geometry is implicit. In addition to studying local Walker geometry, we address a global question raised by the use of spinors.Comment: 41 pages. Typos which persisted into published version corrected, notably at (2.15

Magic N=2 supergravities from hyper-free superstrings

We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level they correspond to the two exceptional N=2 supergravities of the magic square that have the same massless scalar field content as pure N=6 supergravity and N=3 supergravity coupled to three extra vector multiplets. The N=2 model of the magic square that is associated to N=6 supergravity is very peculiar since not only the scalar degrees of freedom but all the bosonic massless degrees of freedom are the same in both theories. All presented hyper-free N=2 models are based on asymmetric orbifold constructions with N=(4,1) world-sheet superconformal symmetry and utilize the 2d fermionic construction techniques. The two exceptional N=2 models of the magic square are constructed via a "twisting mechanism" that eliminates the extra gravitini of the N=6 and N=3 extended supergravities and creates at the same time the extra spin-1/2 fermions and spin-1 gauge bosons which are necessary to balance the numbers of bosons and fermions. Theories of the magic square with the same amount of supersymmetry in three and five space-time dimensions are constructed as well, via stringy reduction and oxidation from the corresponding four-dimensional models.Comment: 27 page

Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions

Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple Euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge