Quantum Corrections and the de Sitter Swampland Conjecture

TL;DR

The paper investigates whether four-dimensional de Sitter solutions can arise in string/M-theory by confronting swampland bounds with explicit equations of motion. It shows that classical no-go results preclude static dS, while quantum corrections can generate dS candidates only if there exists a delicate hierarchy among stringy corrections; however, in generic setups, these backgrounds defy a controlled four-dimensional EFT due to infinite towers of quantum terms and time-dependent fluxes. A parallel analysis in Type IIB with α′ corrections confirms swampland consistency but again points to EFT breakdown for stable dS; an M-theory uplift reveals that full dS isometries require solving highly constrained quantum-corrected EOMs with potentially nonlocal effects. The study suggests that quasi-de Sitter solutions, compatible with swampland bounds and potentially describable within an EFT, may exist, but a robust EFT description of true dS remains elusive and likely requires a precise hierarchy among quantum corrections beyond current constructions.

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.

Figures (1)

• Figure 1: Potential $V(\phi)$ from leading $\alpha'$ correction with positive $\xi$ (i.e. negative $\chi$).