# A minimalistic pure spinor sigma-model in AdS

## TL;DR

This paper constructs a simplified pure spinor sigma-model in AdS space, analyzing its BV phase space and symmetries, and provides a foundation for understanding the string measure in curved backgrounds.

## Contribution

It introduces a minimalistic pure spinor sigma-model in AdS and details its BV phase space action and symmetry structure, simplifying the original complex model.

## Key findings

- The sigma-model's Master Action expansion terminates at quadratic order.
- A degenerate, symmetry-preserving reduction of the model is achieved.
- The action of worldsheet vector fields on the BV phase space is explicitly constructed.

## Abstract

The $b$-ghost of the pure spinor formalism in a general curved background is not holomorphic. For such theories, the construction of the string measure requires the knowledge of the action of diffeomorphisms on the BV phase space. We construct such an action for the pure spinor sigma-model in $AdS_5\times S^5$. From the point of view of the BV formalism, this sigma-model belongs to the class of theories where the expansion of the Master Action in antifields terminates at the quadratic order. We show that it can be reduced to a simpler degenerate sigma-model, preserving the AdS symmetries. We construct the action of the algebra of worldsheet vector fields on the BV phase space of this minimalistic sigma-model, and explain how to lift it to the original model.