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.August 2013 †
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a doublecover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
We give a proof that the pure spinor superstring theory in a novel infinite tension limit, as was discussed recently by Berkovits, reproduces the tree-level scattering amplitudes of the ten-dimensional N = 1 super Yang-Mills in its heterotic version and type II supergravity in its type II version. The Yang-Mills case agrees with the result obtained by Mafra, Schlotterer, Stieberger and Tsimpis.
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