Super-Poincare covariant quantization of the superstring

Abstract

Using pure spinors, the superstring is covariantly quantized.

A new first class algebra, homological perturbation and extension of pure spinor formalism for superstring

“…The proposed prescription enjoys a number of required properties and leads to results which agree with those obtained in the RNS formalism [9] [14] [15].…”

“…The central idea of the pure spinor formalism proposed by Berkovits [9] is that the physical states of superstring can be described as the elements of the cohomology of a BRST-like operator Q given by 2 1) where λ α is a 16-component bosonic chiral spinor satisfying the pure spinor constraints 2) and d α is the spinor covariant derivative given in our convention 3 by…”

“…[dz]V 0 (z), needed for the calculation of n-point amplitudes with n ≥ 4, is characterized by QV 0 = ∂U 0 and was constructed to be of the form [9] [3]…”

“…It is useful to note that B can be written as 9) which follows from the property B 2 = 1. Then, it is easy to see that…”

“…About three years ago, following earlier attempts [3,4,5,6,7,8], Berkovits initiated a new formalism [9] based on the concept of pure spinor (PS) [10,11,12], which is super-Poincaré covariant and posesses a number of remarkable features. The formalism is based on free fields, which form a conformal field theory (CFT) with vanishing central charge.…”