The structure of n-point one-loop open superstring amplitudes

2012/03/31 by Carlos R. Mafra, Oliver Schlotterer · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Helicity #Invariant (physics) #Massless particle #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum electrodynamics #Quantum mechanics #Scattering amplitude #Stirling number #String (physics) #String field theory #Superstring theory #Supersymmetry #Worldsheet #hep-th

paper · pdf · doi:10.1007/jhep08(2014)099

published as JHEP 1408 (2014) 099 · 75 pp, 8 figs, harvmac TeX, v2: published version

openalex publication_date 2014/08/01 · arxiv created 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article we investigate one-loop amplitudes in maximally supersymmetric superstring theory. The non-anomalous part of the worldsheet integrand is presented for any number of massless open-string states. The polarization dependence is organized into the same BRST-invariant kinematic combinations which also govern the leading string correction to tree-level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S₃^n-1 of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang-Mills theory and on the other hand the color tensors at order α′2 of the color-dressed tree amplitude.

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• Unraveling conformal gravity amplitudes