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.
Highlights
Obtaining a background of string theory with a fourdimensional (4d) de Sitter space-time in a well-controlled framework is challenging [1]
The second step is to verify that these supergravity solutions are classical string backgrounds, by satisfying a list of requirements, including a small string coupling gs and a large 6d volume in units of the string length ls
To ensure that a 10d supergravity solution is a classical string background, we identify in practice five requirements to be met: a small gs, large 6d radii ra = 1, ..., 6 in units of ls, quantization of fluxes, a fixed number of orientifolds NOI 5, and lattice quantization conditions
Summary
Obtaining a background of string theory with a fourdimensional (4d) de Sitter space-time in a well-controlled framework is challenging [1]. The second step is to verify that these supergravity solutions are classical string backgrounds, by satisfying a list of requirements, including a small string coupling gs and a large 6d volume in units of the string length ls Studies on this topic were so far rather negative [10, 12,13,14,15] despite possible loopholes, leading to the situation that no stringy classical de Sitter solution has been found, in line with the swampland conjectures. To ensure that a 10d supergravity solution is a classical string background, we identify in practice five requirements to be met: a small gs, large 6d radii ra = 1, ..., 6 in units of ls, quantization of fluxes, a fixed number of orientifolds NOI 5 , and lattice quantization conditions. We obtain the material needed to test, the requirements (1) that would allow this solution to be a classical string background
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