Abstract
In this review we describe a non-trivial 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.
Highlights
Since its inception, it has been clear that General Relativity has many striking similarities to gauge theories
Using string based rules, four-graviton amplitudes with one quantum loop in Einstein gravity were obtained in a form in which the integrands appearing in the expressions were given as products of integrands appearing in gauge theory [25, 55]
The Feynman rules for constructing the diagrams are obtained from the Einstein–Hilbert Lagrangian coupled to matter using standard procedures of quantum field theory. (The reader may consult any of the textbooks on quantum field theory [107, 141] for a derivation of the Feynman rules starting from a given Lagrangian.) For a good source describing the Feynman rules of gravity, the reader may consult the classic lectures of Veltman [138]
Summary
It has been clear that General Relativity has many striking similarities to gauge theories. Using string based rules, four-graviton amplitudes with one quantum loop in Einstein gravity were obtained in a form in which the integrands appearing in the expressions were given as products of integrands appearing in gauge theory [25, 55]. There is, an alternative approach based on obtaining the quantum loop contributions directly from the semi-classical tree-level amplitudes by using D-dimensional unitarity [15, 16, 28, 20, 115] These same methods have been applied to non-trivial calculations in quantum chromodynamics Excellent reviews containing the quantum chromodynamics amplitudes used to obtain corresponding gravity amplitudes are the ones by Mangano and Parke [99], and by Lance Dixon [48] These reviews provide a good description of helicity techniques which are extremely useful for explicitly constructing scattering amplitude in gravity and gauge theories. Applications of string methods to quantum field theory are described in a recent review by Schubert [120]
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