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arXiv · 2211.06731

D=5 Holomorphic Chern-Simons and the Pure Spinor Superstring

Nathan Berkovits
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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 $\hat c$=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 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 $\lambda^\alpha q_\alpha$, where $\lambda^\alpha$ 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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Nathan Berkovits. 2022-11-12. D=5 Holomorphic Chern-Simons and the Pure Spinor Superstring. https://doi.org/10.1007/jhep02(2023)169

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