Pure spinor superstring in AdS_4 x CP^3 with unconstrained ghosts

TL;DR

This paper develops a pure spinor superstring action in AdS_4 x CP^3 using unconstrained ghosts, and verifies its consistency through one-loop finiteness and absence of anomalies.

Contribution

It introduces a new formulation of the pure spinor superstring in AdS_4 x CP^3 with unconstrained ghosts, ensuring consistency and finiteness.

Findings

Confirmed absence of central charge at second order

Demonstrated one-loop finiteness of the effective action

Validated the approach with background field method

Abstract

We construct the action for the pure spinor superstring in the coset description of AdS_4 x CP^3 superspace, using the variables which solve the pure spinor condition. As a test of the consistency of the approach, we use the background field method to verify the absence of central charge at the second order in the expansion and to show the one-loop finiteness of the effective action.