# $\lambda$-Deformation Of The $AdS_{5}\times S^{5}$ Pure Spinor Superstring

## TL;DR

This paper introduces a lambda deformation of the pure spinor superstring in AdS5×S5, preserving integrability and conformal invariance, and provides a method to compute the deformed background supergeometry.

## Contribution

It presents the first lambda deformation of the pure spinor superstring in AdS5×S5, maintaining key symmetries and linking to supergravity solutions.

## Key findings

- Deformation preserves integrability and one-loop conformal invariance.
- Effective action matches the Berkovits-Howe form, enabling supergeometry calculations.
- Deformed background fields satisfy supergravity equations.

## Abstract

The lambda deformation of the pure spinor formalism of the superstring in the $AdS_{5}\times S^{5}$ background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its parent theory. It is also shown that the effective action takes the standard form of the Berkovits-Howe action functional, allowing to calculate the deformed background supergeometry in a straightforward way. The background fields coincide with those of the lambda model of the Green-Schwarz formalism, hence satisfying the same set of supergravity equations of motion.