On Perturbative Gravity and Gauge Theory

We review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for obtaining loop contributions. We also review recent applications of these ideas showing that N=1 D=11 supergravity diverges, and review arguments that N=8 D=4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.Comment: Talk presented at Third Meeting on Constrained Dynamics and Quantum Gravity, Villasimius (Sardinia, Italy) September 13-17, 1999 and at the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, University of Adelaide (Australia) December 13-22, 1999. Latex, 9 page

Two-Loop ϕ4\phi^4-Diagrams from String Theory

Using the {\em cutting and sewing} procedure we show how to get Feynman diagrams, up to two-loop order, of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a properly defined field theory limit, we easily identify the corners of the string moduli space reproducing the correctly normalized field theory amplitudes expressed in the Schwinger parametrization.Comment: 28 pages, 12 figure

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally helicity-violating' amplitudes in N=8 supergravity, and the `all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n < 7, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found `dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N=4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n < 7 N=8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.Comment: Minor errors corrected, Latex, 53 page

One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity

We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization of self-dual gravity in four-dimensional Minkowski space. Our ansatz agrees with explicit computations via D-dimensional unitarity cuts for n less than or equal to 6. It also has the expected analytic behavior, for all n, as a graviton becomes soft, and as two momenta become collinear. The gravity results are closely related to analogous amplitudes in (self-dual) Yang-Mills theory.Comment: Latex2e, 13 pages with 2 encapsulated figures. Minor corrections mad

On the Coupling of Gravitons to Matter

Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of amplitudes with gravitons coupled to vectors or to a single fermion pair. We also present two examples with massive graviton exchange, as would arise in the presence of large compact dimensions. The gauge charges are represented by flavors of dynamical scalars or fermions. This also leads to an unconventional decomposition of color and kinematics in gauge theories.Comment: RevTex, 4 page

The Five Gluon Amplitude and One-Loop Integrals

We review the conventional field theory description of the string motivated technique. This technique is applied to the one-loop five-gluon amplitude. To evaluate the amplitude a general method for computing dimensionally regulated one-loop integrals is outlined including results for one-loop integrals required for the pentagon diagram and beyond. Finally, two five-gluon helicity amplitudes are given.Comment: (talk presented at DPF92), LaTeX, 6 pages, CERN-Th.6733/92, SLAC-PUB-6012, UCLA/92/TEP/4

Perturbative Relations between Gravity and Gauge Theory

We review the relations that have been found between multi-loop scattering amplitudes in gauge theory and gravity, and their implications for ultraviolet divergences in supergravity.Comment: LaTex with package axodraw.sty. 10 pages. Presented by L.D. at Strings 99. Cosmetic changes onl

A technique for loop calculations in non-Abelian gauge theories - with application to five gluon amplitude

A powerful tool for calculations in non-Abelian gauge theories is obtained by combining the background field gauge, the helicity basis and the color decomposition methods. It has reproduced the one-loop calculation of the five-gluon amplitudes in QCD, is applicable to electroweak processes and extendable to two-loop calculations.Comment: Latex 22 pages, 3 figure