The D^6 R^4 term from three loop maximal supergravity

Understand

We consider the D^6 R^4 term which is the leading contribution in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity.

• We calculate the moduli dependent coefficient of this term in 11 dimensional supergravity compactified on T^2.
• Only diagrams that involve the Mercedes skeleton contribute resulting in a compact expression involving an integral over 6 Schwinger parameters.
• We express this integral as an integral over the moduli of an auxiliary T^3.