Abstract
The physical states of D=5 holomorphic Chern-Simons theory correspond to on-shell D=10 open superstring states in the cohomology of q+, where q+ is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these states can be computed either using the usual Ramond-Neveu-Schwarz (RNS) superstring prescription with N=1 worldsheet supersymmetry, or using a topological ĉ=5 string theory with twisted N=2 worldsheet supersymmetry.
It will be argued that the relation between D=5 holomophic Chern-Simons and the RNS superstring is identical to the relation between the pure spinor superstring and the recently constructed B-RNS-GSS superstring which has both N=1 worldsheet supersymmetry and D=10 spacetime supersymmetry. Physical states of the pure spinor superstring correspond to on-shell B-RNS-GSS states which are in the cohomology of λαqα, where λα is a D=10 pure spinor. And scattering amplitudes of these states can be computed either using the full B-RNS-GSS superstring prescription with N=1 worldsheet supersymmetry, or using the pure spinor superstring amplitude prescription with twisted N=2 worldsheet supersymmetry. This should be useful for proving equivalence of the RNS and pure spinor amplitude prescriptions and for clarifying the relation of their multiloop subtleties.
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ArXiv ePrint: 2211.06731
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Berkovits, N. D=5 holomorphic Chern-Simons and the pure spinor superstring. J. High Energ. Phys. 2023, 169 (2023). https://doi.org/10.1007/JHEP02(2023)169
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DOI: https://doi.org/10.1007/JHEP02(2023)169