The KLT equations generically hold for any closed string states, using their Fock space factorization into pairs of open string states. Although not obvious, the gravity amplitudes (10) and (11) have all the required symmetry under interchanges of identical particles. (This is easiest to demonstrate in string theory by making use of an symmetry on the string world sheet.)
In the field theory limit the KLT equations must hold in any dimension, because the gauge theory amplitudes appearing on the right-hand side have no explicit dependence on the space-time dimension; the only dependence is implicit in the number of components of momenta or polarizations. Moreover, if the equations hold in, say, ten dimensions, they must also hold in all lower dimensions since one can truncate the theory to a lower-dimensional subspace.
The amplitudes on the left-hand side of Eqs. (10) and (11) are exactly the scattering amplitudes that one obtains via standard gravity Feynman rules [44, 45, 138]. The gauge theory amplitudes on the right-hand side may be computed via standard Feynman rules available in any modern textbook on quantum field theory [107, 141]. After computing the full gauge theory amplitude, the color-stripped partial amplitudes appearing in the KLT relations (10) and (11), may then be obtained by expressing the full amplitudes in a color trace basis [8, 91, 100, 99, 48]:.
Instead, it is somewhat more convenient to use color-ordered Feynman rules [99, 48, 20] since they directly give the color-stripped gauge theory amplitudes appearing in the KLT equations. These Feynman rules are depicted in Figure 6. When obtaining the partial amplitudes from these Feynman rules it is essential to order the external legs following the order appearing in the corresponding color trace. One may view the color-ordered gauge theory rules as a new set of Feynman rules for gravity theories at tree-level, since the KLT relations allow one to convert the obtained diagrams to tree-level gravity amplitudes  as shown in Figure 6.
To obtain the full amplitudes from the KLT relations in Eqs. (10), (11) and their -point generalization, the couplings need to be reinserted. In particular, when all states couple gravitationally, the full gravity amplitudes including the gravitational coupling constant are:
For the case of four space-time dimensions, it is very convenient to use helicity representation for the physical states [36, 88, 142]. With helicity amplitudes the scattering amplitudes in either gauge or gravity theories are, in general, remarkably compact, when compared with expressions where formal polarization vectors or tensors are used. For each helicity, the graviton polarization tensors satisfy a simple relation to gluon polarization vectors:
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