Quantum Corrections and the de Sitter Swampland Conjecture

TL;DR

This paper investigates the validity of the de Sitter swampland conjecture within string theory by analyzing quantum corrections in M-theory, finding that while classical solutions are ruled out, certain quantum and quasi-de Sitter solutions may still be consistent under specific conditions.

Contribution

It provides a detailed examination of de Sitter solutions in M-theory, incorporating quantum corrections and assessing their compatibility with the swampland criterion, highlighting potential hierarchies and time-dependent scenarios.

Findings

Classical de Sitter solutions are ruled out by the swampland criterion.

Quantum corrections can allow de Sitter solutions under specific constraints.

Quasi-de Sitter solutions may exist with mild time dependence without violating the conjecture.

Abstract

Recently a swampland criterion has been proposed that rules out de Sitter vacua in string theory. Such a criterion should hold at all points in the field space and especially at points where the system is on-shell. However there has not been any attempt to examine the swampland criterion against explicit equations of motion. In this paper we study four-dimensional de Sitter and quasi-de Sitter solutions using dimensionally reduced M-theory. While on one hand all classical sources that could allow for solutions with de Sitter isometries are ruled out, the quantum corrections, on the other hand, are found to allow for de Sitter solutions provided certain constraints are satisfied. A careful study however shows that generically such a constrained system does not allow for an effective field theory description in four-dimensions. Nevertheless, if some hierarchies between the various quantum pieces could be found, certain solutions with an effective field theory description might exist. Such hierarchies appear once some mild time dependence is switched on, in which case certain quasi-de Sitter solutions may be found without a violation of the swampland criterion.