Associators for AdS string amplitude building blocks

TL;DR

This paper demonstrates that associators generate the fundamental building blocks for AdS string amplitudes, extending flat-space recursion relations to AdS and confirming their low-energy expansion properties involving multiple zeta values.

Contribution

It introduces a formalism that lifts associator recursions to the AdS context, providing a new proof of the structure of AdS string amplitude building blocks.

Findings

Associators generate AdS string amplitude building blocks.

The formalism extends flat-space recursion relations to AdS.

All-order relations for integral expressions are established.

Abstract

We show that building blocks for open- and closed-string amplitudes on AdS are generated by the Drinfeld and Deligne associator, respectively. Our formalism lifts the known associator recursions for flat-space string amplitudes to the AdS picture. This delivers another proof that the AdS building blocks admit low-energy expansions with (single-valued) multiple zeta values as coefficients and provides all-order relations for the integral expressions.