A THEORY OF CONFORMAL GRAVITY AND CONFORMAL SUPERGRAVITY

We shall establish a theory of conformal gravity by taking the conformal group SO(4,2)as the gauge group. The Lagrangian of the theory is a Yang-Mills-like one, which contains theLagrangian of Einstein-Cartan gravity and the cosmological constant, and is invariant underthe Weyl conformal mapping. Based on the conformal gravity, a conformal supergravity will be introduced as a gaugetheory of the superconformal group SU(2,2|1). The Lagrangian is also taken as a Yang-Mills-like supertrace invariant and contains two massless Rarita-Schwinger fields and anAbelian gauge field which couple with the conformal gravity in a definite way.