CONFORMAL SCALAR FIELDS IN CURVED 3-DIMENSIONAL SPACE

We consider the effect of quantum corrections to a conformally invariant field theory for a scalar field phi in curved three-dimensional spacetime. In addition to the conformally invariant kinetic action there is a lambdaphi6 interaction term. The analysis is most easily performed in a space of constant curvature using a formalism of Drummond. Explicit calculation to order lambda3 shows that all divergences can be removed by renormalizing the cosmological constant and wavefunction; no divergences appear that require the introduction of term;s proportionsl to Rphi2 or square-root R phi4.