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High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT
Abstract:
The recursive calculation of Selberg integrals by Aomoto and Terasoma using
the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an
auxiliary point and facilitates the recursive evaluation of string amplitudes
at genus zero: open-string N-point amplitudes can be obtained from those at N-1
points. We establish a similar formalism at genus one, which allows the
recursive calculation of genus-one Selberg integrals using an extra marked
point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby
genus-one Selberg integrals are related to genus-zero Selberg integrals.
Accordingly, N-point open-string amplitudes at genus one can be obtained from
(N+2)-point open-string amplitudes at tree level. The construction is related
to and in accordance with various recent results in intersection theory and
string theory.
