Relating the RNS and Pure Spinor Formalisms for the Superstring

Recently, the superstring was covariantly quantized using the BRST-like operator $Q = \\oint \\lambda^\\alpha d_\\alpha$ where $\\lambda^\\alpha$ is a pure spinor and $d_\\alpha$ are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and $\\eta_0$ ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a $b$ ghost in the pure spinor formalism which might be useful for loop amplitude computations.