Superstring amplitudes and the associator
J. M. Drummond, E. Ragoucy
TL;DR
The paper uncovers a deep Hopf-algebraic pattern in the α' expansion of tree-level open superstring amplitudes, recasting the structure in terms of motivic multiple zeta values and their coaction. It shows that the pattern is intimately linked to the Drinfeld associator from the Knizhnik-Zamolodchikov equation, and that, at least for the four-point case, the associator determines the amplitude. This leads to a basis-independent description where depth-one zeta values fix higher-depth coefficients, and connects open-string amplitudes to universal monodromy through the Ihara action. The work also clarifies how closed-string amplitudes inherit constrained zeta-value structures via KLT, with implications for IIB duality and modular forms, and demonstrates the four-point result explicitly from the associator.
Abstract
We investigate a pattern in the $α'$ expansion of tree-level open superstring amplitudes which correlates the appearance of higher depth multiple zeta values with that of simple zeta values in a particular way. We rephrase this relationship in terms of the coaction on motivic multiple zeta values and show that the pattern takes a very simple form, which can be simply explained by relating the amplitudes to the Drinfel'd associator derived from the Knizhnik-Zamolodchikov equation. Given this correspondence we show that, at least in the simplest case of the four-point amplitude, the associator can be used to extract the form of the amplitude.