KK-like relations of α′ corrections to disk amplitudes
KK-like relations of α′ corrections to disk amplitudes
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′
2ζ
2 corrections is encoded in the descent algebra.
hep-th, math.CO
Mafra, Carlos R.
5a40c14f-0ddb-4c0c-9ce5-acabc537cd01
2 March 2022
Mafra, Carlos R.
5a40c14f-0ddb-4c0c-9ce5-acabc537cd01
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 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′
2ζ
2 corrections is encoded in the descent algebra.
Text
2108.01081v2
- Author's Original
Text
Mafra2022_Article_KK-likeRelationsOfΑCorrections
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Accepted/In Press date: 15 February 2022
Published date: 2 March 2022
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© 2022, The Author(s).
Keywords:
hep-th, math.CO
Identifiers
Local EPrints ID: 467691
URI: http://eprints.soton.ac.uk/id/eprint/467691
ISSN: 1029-8479
PURE UUID: 9969647e-e142-4fa0-a830-8f4e0a8f705d
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Date deposited: 19 Jul 2022 16:51
Last modified: 17 Mar 2024 03:33
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