Unified Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in four dimensions

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