One-loop Conformal Invariance of the Type II Pure Spinor Superstring in a Curved Background

TL;DR

This paper demonstrates that the one-loop beta functions of the Type II pure spinor superstring vanish in a curved background, confirming conformal invariance at the quantum level due to classical BRST symmetry.

Contribution

It proves the one-loop conformal invariance of the Type II pure spinor superstring in curved backgrounds based on classical BRST symmetry.

Findings

One-loop beta functions vanish in generic supergravity backgrounds.

Conformal invariance is maintained at the quantum level.

Classical BRST symmetry ensures quantum consistency.

Abstract

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.