Color-dressed string disk amplitudes and the descent algebra

Abstract

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. Comparing both definitions suggests a duality between permutations in the inverse descent algebra and kinematics from the higher $\alpha'$ sector of string disk amplitudes. We analyze the symmetries of the $\alpha'$ disk corrections and obtain a new decomposition for them, leading to their dimensions given by sums of Stirling cycle numbers. The descent algebra also leads to the interpretation that the ${\alpha'}^2\zeta_2$ correction is orthogonal to the field-theory amplitudes as well as their respective tails of BCJ-preserving interactions. In addition, we show how the superfield expansion of BRST invariants of the pure spinor formalism corresponding to ${\alpha'}^2$ corrections are encoded in the descent algebra.

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ORCID for Carlos R. Mafra: orcid.org/0000-0001-9842-9654

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