Quantum Consistency of the Superstring in AdS_5 x S^5 Background

TL;DR

This paper proves that the pure spinor superstring in AdS_5 x S^5 background maintains BRST and conformal invariance at all quantum orders, establishing its consistency for string theory in this setting.

Contribution

It demonstrates quantum BRST and conformal invariance of the pure spinor superstring in AdS_5 x S^5 using cohomology, and shows the existence of an infinite set of non-local charges.

Findings

BRST invariance at all orders in perturbation theory

Conformal invariance at the quantum level

Existence of infinite non-local BRST-invariant charges

Abstract

Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS_5 x S^5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.