The closed-string 3-loop amplitude and S-duality

Understand

The low-energy limit of the four-point 3-loop amplitude (including its overall coefficient) is computed in both type IIA and IIB superstring theories using the pure spinor formalism.

• The result is shown to agree with the prediction of the coefficient for the type IIB $D^6 R^4$ interaction made by Green and Vanhove based on S-duality considerations.