Exploring Pure Spinor String Theory on AdS_4 x CP^3

TL;DR

This work builds a BRST-enhanced pure spinor formulation of the superstring on $AdS_4\times \mathbb{CP}^3$, showing its equivalence to a topological A-model on the fermionic coset $Osp(6|4)/SO(6)\times Sp(4)$ via a BRST-trivial deformation. It then constructs a linear gauged sigma-model (GLSM) whose large-volume limit reproduces the A-model, and analyzes the Coulomb/Higgs branches to expose the vacuum structure and zero-radius phases. A principal chiral model for the same supergroup is developed and connected to the A-model through gauge fixing and integrating out auxiliary fields, while D-brane boundary conditions are explored to relate open-string sectors to 3D gauge theories on $AdS_3$ and potential M-theory realizations. The paper provides a coherent framework linking pure spinor strings, topological strings, GLSMs, and boundary gauge dynamics in the $AdS_4/CFT_3$ context, and outlines concrete directions for BRST cohomology, amplitudes, and holographic boundary dynamics.

Abstract

In this paper we formulate the pure spinor superstring theory on AdS_4 x CP^3. By recasting the pure spinor action as a topological A-model on the fermionic supercoset Osp(6|4)/SO(6)xSp(4) plus a BRST exact term, we prove the exactness of the sigma-model. We then give a gauged linear sigma-model which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible D-brane boundary conditions and the principal chiral model for the fermionic supercoset.