Covariant Quantization of Superstrings Without Pure Spinor Constraints

Abstract

We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST charge, is treated as a new generator with a new b − c system. We construct a nilpotent BRST current, an anomalous ghost current and an anomaly-free energy-momentum tensor. For open superstrings, we find the correct massless spectrum. In addition, we construct a Lorentz invariant B-field to be used for the computation of the integrated vertex operators and amplitudes.

Free fermion resolution of supergroup WZNW models

“…But for a long time it has not been clear how to quantize these field theories while keeping the target space supersymmetry manifest. It was only recently that the pure spinor approach closed this gap to some extent [86,87]. Although substantial progress has been made on certain aspects of the pure spinor formulation, there exist a variety of open conceptual issues, in particular when curved backgrounds are involved.…”

The Massless Spectrum of Covariant Superstrings

“…In particular, our results agree with the work of Berkovits and collaborators [2], who obtains the correct field equations for the massless states γ αβ mnrpq D α A β = 0, but defines physical states by only the BRST condition on the unintegrated vertex U (1) = λ α A α (x, θ) in terms of pure spinors λ α . In their work the superfields A m and W α (the latter is denoted by A α in [1]) of the open string are expressed in term of A α by the relations of d = 10 superspace,…”

“…eq. (1.2) in [1]) and the field B zz (z) have different grading 4 . For instance, the BRST current can be decomposed in the following pieces j…”

Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring

“…The definition of (1.8) for the unconstrained Λ α might be useful for understanding the relation with "extended" versions of the pure spinor formalism such as [20][21][22][23] in which the spinor ghosts were unconstrained. After defining Γ m and Γ m as in (1.5), the RNS γ ghost only appears in even powers so it is convenient to define a new ghost variable γ ≡ (γ) 2 .…”