A-cycle integrals at genus one satisfy linear differential equations whose Picard iterations yield all-order alpha-prime expansions in iterated Eisenstein integrals, with cusp values given by disk integrals.
String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
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We compute one-loop amplitudes in six-dimensional Yang-Mills theory with half-maximal supersymmetry from first principles: imposing gauge invariance and locality on an ansatz made from string-theory inspired kinematic building blocks yields unique expressions for the 3- and 4-point amplitudes. We check that the results are reproduced in the field-theory limit $\alpha' \rightarrow 0$ of string amplitudes in K3 orbifolds, using simplifications made in a companion string-theory paper 1603.05262.
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One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
A-cycle integrals at genus one satisfy linear differential equations whose Picard iterations yield all-order alpha-prime expansions in iterated Eisenstein integrals, with cusp values given by disk integrals.