Intricacies of classical de Sitter string backgrounds

TL;DR

This paper investigates two recent 10-dimensional supergravity de Sitter solutions to determine if they can be extended to full classical string backgrounds, revealing key challenges and subtleties in realizing such solutions.

Contribution

It provides a detailed analysis of two new de Sitter solutions, developing tools to test their viability as classical string backgrounds and highlighting the difficulties involved.

Findings

Both solutions fail to meet all necessary criteria simultaneously.

Explicit values illustrate the challenges in promoting supergravity solutions to string backgrounds.

The analysis emphasizes subtleties and the relation to scale separation issues.

Abstract

Up-to-date, there is no known example of a classical de Sitter solution of string theory, despite several good candidates. We consider here two newly discovered 10d supergravity de Sitter solutions, and analyse in great detail whether they can be promoted to classical string backgrounds. To that end, we identify five requirements to be met, and develop the necessary 10d tools to test the solutions. Eventually, they both fail to verify simultaneously all requirements, in spite of positive partial results. The explicit values obtained offer a clear illustration of the situation, and the analysis highlights various subtleties. We finally discuss the relation to the problem of scale separation.