Amplitude recursions with an extra marked point

DOI10.4310/CNTP.2022.V16.N1.A3arXiv1912.09927WikidataQ114020848 ScholiaQ114020848MaRDI QIDQ6331533

Publication date: 20 December 2019

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.

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Wave scattering in solid mechanics (74J20) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Strings (74K05)

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