Introduction: string theory and Type IIB supergravity

String theory not only provides a consistent quantization for gravity, but even at the classical level gives a new insight into the classical gravity.

In the pure spinor formalism, classical SUGRA solutions are encoded in classical string worldsheet theories. To find a SUGRA solution is the same as to find a classical 2-dimensional -model action with certain properties:

10d classical Type IIB SUGRA solutions

-models with some special properties

The notion of vertex operators belongs to the deformation theory. Let us consider a particular SUGRA solution, and the corresponding -model. Then consider a small deformation of both. Infinitesimal deformations are described by vertex operators. If we want to describe finite but small variations, there is some algebraic structure on the space of vertex operators, which tells us how to superimpose them.