Stability of Antisymmetric Tensor Fields of Chern-Simons Type in AdS Spacetime

TL;DR

This paper investigates the stability of massive antisymmetric tensor fields with Chern-Simons action in AdS spacetime, demonstrating positive energy solutions and the absence of alternative stable boundary conditions.

Contribution

It provides a comprehensive analysis of stability for these tensor fields in AdS, highlighting the uniqueness of stable solutions with positive energy and standard boundary conditions.

Findings

Existence of a complete set of positive-energy solutions

Scalar products are well-defined and conserved

No alternative stable solutions with different boundary conditions

Abstract

Stability of massive antisymmetric tensor fields with the Chern-Simons type action in anti de Sitter spacetime is studied. It is found that there exists a complete set of solutions whose energy is conserved and positive definite if the mass is positive. Scalar products of the solutions are shown to be well-defined and conserved. In contrast to the previously studied scalar field case there is no other set of stable solutions with a different kind of boundary condition.