Superstring amplitudes and the associator

Abstract

We investigate a pattern in the ${\alpha }^{\prime }$ 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.

20 pages, 1 figure

References in corpus (2)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Minimal Basis for Gauge Theory Amplitudes

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