Amplitude recursions with an extra marked point

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.

v2: replaced with published version

References in corpus (4)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

Cited by in corpus (5)

• Tree-level amplitudes from the pure spinor superstring
• A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory
• Open-string integrals with multiple unintegrated punctures at genus one
• Open & Closed vs. Pure Open String One-Loop Amplitudes
• A construction of single-valued elliptic polylogarithms