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Perturbative quantum gravity and its relation to gauge theory. (English) Zbl 1023.83010

Summary: In this review we describe a nontrivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

MSC:

83C45 Quantization of the gravitational field
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
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References:

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