Such relations, however, do not hold in any of the standard formulations of gravity. For example, the three-vertex in the standard de Donder gauge (3) contains traces over gravitons, i.e. a contraction of indices of a single graviton. For physical gravitons the traces vanish, but for gravitons appearing inside Feynman diagrams it is in general crucial to keep such terms. A necessary condition for obtaining a factorizing three-graviton vertex (4) is that the “left” indices never contract with the “right” indices. This is clearly violated by the three-vertex in Eq. (3). Indeed, the standard formulations of quantum gravity generate a plethora of terms that violate the heuristic relation (1).
In Section 4 the question of how one rearranges the Einstein action to be compatible with string theory intuition is returned to. However, in order to give a precise meaning to the heuristic formula (1) and to demonstrate that scattering amplitudes in gravity theories can indeed be obtained from standard gauge theory ones, a completely different approach from the standard Lagrangian or Hamiltonian ones is required. This different approach is described in the next section.
© Max Planck Society and the author(s)