Towards de Sitter Space in String Theory

• Applicant: Professor Dr. Arthur Hebecker
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 552080800

At the perturbative level, string theory provides a consistent UV completion of quantum gravity. Important achievements include the finiteness of loop effects and the calculation of black hole entropies in simple cases. However, to claim that string theory can UV-complete gravity in the real world, more is required: One needs to compactify the originally 10-dimensional theory down to 4d while realising the effective field theory of the Standard Model of particle physics. Although the enormous number of such compactifications prevents an exhaustive search, significant progress has been made in finding models with the correct basic structure, including gauge group and matter content. A key problem that has remained unsolved is the realisation of a positive cosmological constant, i.e. de Sitter space, or, more generally, of a 4d Universe with accelerated cosmological expansion. What is worse, some of the most successful string-theoretic de Sitter models have recently come under severe pressure. This is one of the results of the so-called Swampland Program, which proposes to search for general constraints on what can or cannot be realised within the set of all string compactifications. The group of the applicant has significantly contributed to quantifying the ‘control issues’ of the so far leading de Sitter models. At present, we cannot be certain that they work because of effects of an infinite series of unknown and unsuppressed corrections. As a result of these developments, it is one of the most important open questions in string theory whether and how cosmological acceleration can be realised. The present project aims at advancing this key research direction by studying an alternative possibility of realising de Sitter space known as ‘F-term uplift’. The key underlying idea is to search for minima with small positive vacuum energy in a potential landscape over the high-dimensional space of complex deformations of the compact (Calabi-Yau) geometry taking us from 10d to 4d. While this basic proposal is well-known, it is hard to demonstrate explicitly that it works because the necessary calculations are highly complex. Due to recent computational advances, there has been progress in simplified settings. Based on this and on novel ideas for how to treat string-derived scalar potentials and specifically the F-term uplift with analytical methods, we want to make progress towards realising the F-term uplift explicitly. We aim at establishing this mechanism as the new leading candidate for building de Sitter vacua in string theory. Alternatively, we will pin down and quantify the possible problems making this impossible. Either outcome would be very important for the whole field of string phenomenology, i.e. for the enterprise of relating strings to the real world.

• DFG Programme: Research Grants