A Note on Infinite Symmetries of a Free Scalar on AdS Backgrounds and the Breitenlohner-Freedman Bound

TL;DR

This paper explores the infinite-dimensional symmetries of a free scalar field in Anti de-Sitter space, analyzing boundary conditions and their relation to the Breitenlohner-Freedman bound.

Contribution

It demonstrates the construction of infinite symmetries for a free scalar in AdS backgrounds and verifies boundary term conditions for Noether's theorem.

Findings

Infinite symmetries generated by space-time isometries.

Boundary terms in Noether currents vanish at the boundary.

Insights into stability bounds for scalar fields in AdS.

Abstract

We construct infinite dimensional symmetries of a complex, free scalar field on curved space-times generated by isometries of the space-time. We use the Anti de-Sitter backgrounds as an example and check that the boundary terms appearing in the Noether current satisfy the requirement of Noether's theorem that they vanish at the boundary.