Cosmological constant, dilaton field and Freund-Rubin compactification

TL;DR

This paper investigates the effects of a dilaton field and cosmological constant on Freund-Rubin compactification, revealing conditions for stable anti-de Sitter spacetimes in string theory contexts.

Contribution

It analyzes the stability of compactified spacetimes with a dilaton field, highlighting the stability of anti-de Sitter vacua in superstring theory scenarios.

Findings

Minkowski and de Sitter spacetimes occur without the dilaton field.

Dilaton field restricts spacetime to anti-de Sitter.

Anti-de Sitter vacuum is stable at linear level for $a=1$.

Abstract

We discuss the Freund-Rubin compactification with cosmological constant and the dilaton field, and examine the stability of the spacetimes at the low energy. The Minkowski or de Sitter spacetime can be obtained if the dilation field is turned off while we observe that the dilaton field does not permit such spacetimes but only the anti-de Sitter spacetime. The stability of the spacetime depends on the dimensions of the spacetime and the compactified space and the coupling constant of the dilaton field $a$. In the $a=1$ case, which corresponds to superstring theories, the anti-de Sitter vacuum is stable at least in the linear level.