O(N)-SCALAR MODEL IN CURVED SPACETIME WITH BOUNDARIES - A RENORMALIZATION-GROUP APPROACH

We discuss the volume and surface running couplings for O(N) scalar th eory in curved spacetime with boundaries. The IR limit of the theory-i n which it becomes asymptotically conformally invariant-is studied, an d the existence of IR fixed points for all couplings (also in D=4-epsi lon dimensions) is shown. For N=4 the behaviour of some gravitational couplings in the IR limit is changing qualitatively, from a growth for N less than or equal to 4 to a decrease for N>4. The non-local renorm alization group (RG) improved effective action, account being taken of the boundary terms, is found. For O(N) scalar theory and for scalar e lectrodynamics, the RG improved effective action in the spherical cap is constructed. The relevance of surface effects for the effective equ ations of motion for the spherical cap is considered (which may be imp ortant in quantum cosmology). Some preliminary remarks on the connecti on with Casimir theory are also given. (C) 1996 Academic Press, Inc.