One-loop Conformal Invariance of the Type II Pure Spinor Superstring in   a Curved Background
  We compute the one-loop beta function for the Type II superstring using the pure spinor formalism in a generic supergravity background. It is known that the classical pure spinor BRST symmetry puts the background fields on-shell. In this paper we show that the one-loop beta functions vanish as a consequence of the classical BRST symmetry of the action. 
Oscar A. Bedoya, Osvaldo Chandia