We study the properties of the vertex operator for the β-deformation of the superstring in AdS 5 ×S 5 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.

Relation between semiclassical analyses of Green-Schwarz and pure spinor formalisms in an AdS 5 × S 5 background is clarified. It is shown that the two formalisms have identical semiclassical partition functions for a simple family of classical solutions. It is also shown that, when the classical string is furthermore rigid, this in turn implies that the two formalisms predict the same one-loop corrections to spacetime energies.

In this work, we use the framework of effective field theory to couple Einstein’s gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one-graviton exchange. Studying the renormalization group functions, we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational interaction. Our result indicates that gravitational corrections do not alter the running behavior of the gauge coupling constants, even if massive particles are present.

In this paper we study the pure spinor formulation of the superstring in AdS 5 × S 5 around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background.