Notes on β-deformations of the pure spinor superstring in AdS5×S5

We study the properties of the vertex operator for the β-deformation of the superstring in AdS5×S5 in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal β-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description.