Figure 1:
The Feynman propagator and three and fourpoint vertices in Einstein gravity. 

Figure 2:
Sample gravity treelevel Feynman diagrams. The lines represent any particles in a gravity theory. 

Figure 3:
Sample looplevel Feynman diagrams. Each additional loop represents an extra power of Planck’s constant. 

Figure 4:
An example of a fiveloop diagram. 

Figure 5:
String theory suggests that the threegraviton vertex can be expressed in terms of products of threegluon vertices. 

Figure 6:
The colorordered gauge theory Feynman rules for obtaining treelevel scattering amplitudes for gravity coupled to matter, via the KLT equations. The Greek indices are spacetime ones and the Latin ones are group theory ones. The curly lines are vectors, dotted ones scalars, and the solid ones fermions. 

Figure 7:
The three colorordered Feynman diagrams contributing to the QCD partial amplitude in Eq. (15). 

Figure 8:
As two momenta become collinear a gravity amplitude develops a phase singularity that can be detected by rotating the two momenta around the axis formed by their sum. 

Figure 9:
The twoparticle cut at one loop in the channel carrying momentum . The blobs represent tree amplitudes. 

Figure 10:
Two examples of generalized cuts. Double twoparticle cuts of a twoloop amplitude are shown. This separates the amplitude into a product of three tree amplitudes, integrated over loop momenta. The dashed lines represent the cuts. 

Figure 11:
The oneloop box integral. Each internal line in the box corresponds to one of the four Feynman propagators in Eq. (51). 

Figure 12:
The planar and nonplanar scalar integrals, appearing in the twoloop amplitudes. Each internal line represents a scalar propagator. 

Figure 13:
Starting from an loop planar diagram representing an integral function, an extra line may be added to the inside using this rule. The two lines on the left represent two lines in some loop diagram. 
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