The closed-string 3-loop amplitude and S-duality
arXiv:1308.6567 · doi:10.1007/JHEP10(2013)217
Abstract
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.
26 pages, harvmac. v3: factor of 3 in section 3.3 corrected, updated abstract and dropped Z_3-symmetry argument