Remarks on positive energy vacua via effective potentials in string theory

TL;DR

This paper investigates warped compactifications in string/M theory, focusing on effective potentials to analyze the stability and existence of metastable de Sitter vacua, especially considering the dynamics of the internal metric's conformal factor.

Contribution

It provides new existence and stability results for metastable de Sitter vacua in non-supersymmetric string theory setups using effective potential methods.

Findings

Proved existence of solutions with slowly varying warp factors.

Analyzed stability of these solutions.

Identified a family of metastable de Sitter vacua.

Abstract

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is explored, and such instabilities are investigated in the context of de Sitter vacua. We prove existence results for the equations of motion in the case of a slowly varying warp factor, and the stability of such solutions is also addressed. These solutions are a family of meta-stable de Sitter vacua from type IIB string theory in a general non-supersymmetric setup.