Cornering the unphysical vertex

TL;DR

This paper investigates nonphysical vertex operators in the pure spinor formalism of AdS5xS5, revealing that certain BRST deformations in flat space relate to nontrivial backgrounds like the linear dilaton, and emphasizing the importance of beta-function conditions.

Contribution

It demonstrates that the BRST operator can be nontrivially deformed independently of the worldsheet action, uncovering new insights into background characterization beyond classical BRST symmetry.

Findings

Nonphysical vertex operators lead to nontrivial BRST deformations in flat space.

Some deformations correspond to the linear dilaton background.

Nonphysical deformations have nonzero one-loop beta-function, affecting background consistency.

Abstract

In the classical pure spinor worldsheet theory of AdS5xS5 there are some vertex operators which do not correspond to any physical excitations. We study their flat space limit. We find that the BRST operator of the worldsheet theory in flat space-time can be nontrivially deformed without deforming the worldsheet action. Some of these deformations describe the linear dilaton background. But the deformation corresponding to the nonphysical vertex differs from the linear dilaton in not being worldsheet parity even. The nonphysically deformed worldsheet theory has nonzero beta-function at one loop. This means that the classical Type IIB SUGRA backgrounds are not completely characterized by requiring the BRST symmetry of the classical worldsheet theory; it is also necessary to require the vanishing of the one-loop beta-function.