The super-Yang–Mills tree amplitudes turn out to have a particularly simple sewing formula ,any dimension (though some care is required to maintain the total number of physical states at their four-dimensional values so as to preserve the supersymmetric cancellations). The simplicity of this result is due to the high degree of supersymmetry.
Using the gauge theory result (55), it is a simple matter to evaluate Eq. (54). This yields:
Applying Eq. (56) at one loop to each of the three kinematic channels yields the one-loop four graviton amplitude of supergravity,. The gravitational coupling has been reinserted into this expression. The scalar integrals are defined in Eq. (51), inserting . This is a standard integral appearing in massless field theories; the explicit value of this integral may be found in many articles, including Refs. [69, 27]. This result actually holds for any of the states of supergravity, not just external gravitons. It is also completely equivalent to the result one obtains with covariant Feynman diagrams including Fadeev–Popov  ghosts and using regularization by dimensional reduction . The simplicity of this result is due to the high degree of supersymmetry. A generic one-loop four-point gravity amplitude can have up to eight powers of loop momenta in the numerator of the integrand; the supersymmetry cancellations have reduced it to no powers.
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