D=5 holomorphic Chern-Simons and the pure spinor superstring

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.

B-RNS-GSS heterotic string in curved backgrounds

“…This untwisting procedure shifts the conformal anomaly contribution of the (Λ α , wα) variables from +32 to −16, so the untwisted BRST operator is no longer nilpotent. To make this untwisting procedure consistent at the quantum level, one needs to add to the RNS variables not only the (θ α , pα, Λ α , wα) variables, but also the non-minimal variables (Λα, w α , Rα, S α ) where (Λα, w α ) and (Rα, S α ) are 32 leftmoving bosons and fermions of conformal weight (0, 1)[10]. The non-minimal BRST operator is obtained…”