Towards Hypergravity

Abstract

The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common features as well as differences of the Yang-Mills theories and gauge theories of gravity is carried out. In particular, we consider the following issues: (i) Representations of the relevant global symmetry on states and on fields, (ii) Relations between the relevant global and local symmetries, (iii) Representations of the local symmetries on states and fields, (iv) Dimensional analysis of the gauge algebra generators and the number of counter terms, and (v) Coupling to the spinorial matter fields. We conclude, that various difficulties on the gravity side can be overcome by considering the below outlined Hypergravity gauge theory, that to some extend parallels the string/membrane theories. This theory is based on an infinite Lie algebraic structure of generators that transforms as "states" of the infinite-dimensional irreducible representation of the $\bar{SL}(4,R)$ subgroup of the Group of General Coordinate Transformations of R^4. The metric-affine and Poincaré gauge theories of gravity are obtained through a spontaneous symmetry breaking mechanism, with the metric field as nonlinear symmetry realizer.