A tree-based algorithm converts modular graph forms into equivariant iterated Eisenstein integrals, is implemented for topologies up to four vertices, and is used to extract the alpha'^8 zeta3 zeta5 term of the four-graviton amplitude.
Building blocks of closed and open string amplitudes
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abstract
In this text we review various relations between building blocks of closed and open string amplitudes at tree-level and genus one. We explain that KLT relations between tree-level closed and open string amplitudes follow from the holomorphic factorisation of conformal correlation functions on conformal blocks. We give a simple hands-on evaluation of the $\alpha'$-expansion of tree-level closed string amplitudes displaying the special single-valued nature of the coefficients. We show that the same techniques can be used also at genus-one, where we give a new proof of the single-valued nature of the coefficients of 2-point closed string amplitudes. We conclude by giving an overview of some open problems.
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From Modular Graph Forms to Iterated Integrals
A tree-based algorithm converts modular graph forms into equivariant iterated Eisenstein integrals, is implemented for topologies up to four vertices, and is used to extract the alpha'^8 zeta3 zeta5 term of the four-graviton amplitude.