KK-like relations of α′ corrections to disk amplitudes

• Published in: The journal of high energy physics 2022-03, Vol.2022 (3), p.12-27, Article 12
• Main Author: Mafra, Carlos R.
• Format: Article
• Language: English
• Subjects: Algebra; Amplitudes; Classical and Quantum Gravitation; Color; Combinatorics; Elementary Particles; High energy physics; Invariants; Kinematics; Permutations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering Amplitudes; Stirling cycle; String Theory; Superstrings and Heterotic Strings
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2022)012

A bstract Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding permutations. Decomposing the color traces into symmetrized traces and structure constants, the color-dressed permutations define BRST-invariant permutations , which we show are elements of the inverse Solomon descent algebra and we find a closed formula for them. We then present evidence that these permutations encode KK-like relations among the different α ′ corrections to the disk amplitudes refined by their MZV content. In particular, the number of linearly independent amplitudes at a given α ′ order and MZV content is given by (sums of) Stirling cycle numbers. In addition, we show how the superfield expansion of BRST invariants of the pure spinor formalism corresponding to α ′ 2 ζ 2 corrections is encoded in the descent algebra.