# Manifestly T-dual formulation of AdS space

## TL;DR

This paper develops a T-dual formulation of AdS space using doubled geometry, revealing a connection between AdS and dS spaces through algebraic structures and preserving physical coordinates.

## Contribution

It introduces a manifestly T-dual framework for AdS spaces with a novel affine doubled algebra incorporating Ramond-Ramond flux.

## Key findings

- Left momentum resides in AdS space.
- Right momentum resides in dS space.
- Doubled coordinates are preserved under reduction constraints.

## Abstract

We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates.