Twisted de Rham theory for string double copy in AdS

TL;DR

This paper proves a double-copy relation for string amplitudes in AdS space using a novel noncommutative twisted de Rham theory, extending flat space techniques to curved backgrounds.

Contribution

It introduces a noncommutative twisted de Rham framework to establish the AdS double-copy relation for string amplitudes, generalizing flat space methods.

Findings

Derived the intersection number of open-string contours in noncommutative twisted homology.

Identified the inverse of the intersection number as the AdS double-copy kernel.

Validated the double-copy relation for all-order AdS curvature corrections.

Abstract

This work is motivated by the recent evidence for a double-copy relationship between open- and closed-string amplitudes in Anti-de Sitter (AdS) space. At present, the evidence has the form of a double-copy relation for string-amplitude building blocks, which are combined using the multiple-polylogarithm (MPL) generating functions. These generate MPLs relevant for all-order AdS curvature corrections of four-point string amplitudes. In this paper, we prove this building-block double copy using a new, noncommutative version of twisted de Rham theory. In flat space, the usual twisted de Rham theory is already known to be a natural framework to describe the Kawai-Lewellen-Tye (KLT) double-copy map from open- to closed-string amplitudes, in which the KLT kernel can be computed from the intersections of the open-string amplitude integration contours. We formulate twisted de Rham theory for noncommutative-ring-valued differential forms on complex manifolds and use it to derive the intersection number of two open-string contours, which are closed in the noncommutative twisted homology sense. The inverse of this intersection number is precisely the AdS double-copy kernel for the four-point open- and closed-string generating functions.