Decoupling of unphysical states in the minimal pure spinor formalism I

Abstract

This is the first of a series of two papers where decoupling of unphysical states in the minimal pure spinor formalism is investigated. The multi-loop amplitude prescription for the minimal pure spinor superstring formulated in hep-th/0406055 involves the insertion of picture changing operators in the path integral. These operators are BRST closed in a distributional sense and depend on a number of constant tensors. One can trace the origin of these insertions to gauge fixing, so the amplitudes are formally independent of the constant tensors. We show however by explicit tree-level and one-loop computations that the picture changing operators are not BRST closed inside correlators and the amplitudes do depend on these constant tensors. This is due to the fact that the gauge fixing condition implicit in the existing minimal amplitude prescription is singular and this can lead to Lorentz violation and non-decoupling of BRST exact states. As discussed in hep-th/0406055, a manifestly Lorentz invariant prescription can be obtained by integrating over the constant tensors and in the sequel to this paper, it is shown that when one includes these integrations unphysical states do decouple to all orders despite the fact that the PCO's are not BRST closed inside correlators.

77 pages (51 pages + appendices), added hyperrefs

References in corpus (15)

• ICTP Lectures on Covariant Quantization of the Superstring
• R^4, purified
• New Higher-Derivative $R^4$ Theorems
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Explaining the Pure Spinor Formalism for the Superstring
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• BRST quantization of the pure spinor superstring
• Decoupling of unphysical states in the minimal pure spinor formalism II

Cited by in corpus (5)

• The closed-string 3-loop amplitude and S-duality
• Pure spinor superfields -- an overview
• A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
• Pure Spinor Integration from the Collating Formula
• Pure spinor computation towards open string three-loop