The 1/N Expansion in Supergravity and R('2) Terms in General Relativity.
Abstract
There are three very different approaches to the quantization of gravity. One is to solve the canonically quantized theory nonperturbatively. The other two approaches are to modify Einstein's relativity in some way or to modify our perturbation approach. One possible modification of general relativity is supergravity. This paper will examine the renormalization properties of supergravity coupled to N multiplets of matter. The first part of the paper will discuss how N matter multiplets can be introduced into a supergravity theory in a supersymmetric way. It will then be shown that the theory can be made finite to lowest order in 1/N expansion with the addition of a fourth order gravity term (and its supersymmetric partners). We see then that renormalization considerations of vastly different theories including gravity all lead to the inclusion of fourth order gravitational terms. It is therefore interesting to explore some of the other ramifications fourth order terms have in gravitational theories. The last chapter of this paper discusses the implications of fourth order gravity terms on the stability of singular solutions to the gravitational equations. In particular, it is shown that the Kerr solution, which is a singular solution to Einstein's equations (and hence to the fourth order theory as well since all solutions to the second order theory are also solutions to the fourth order theory) is not a stable solution to the fourth order theory. This suggests that the fourth order theory may have a nonsingular stable solution which is not a solution of the second order theory.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 1987
- Bibcode:
- 1987PhDT.......161H
- Keywords:
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- Physics: Elementary Particles and High Energy