4D de Sitter from String Theory via 6D Supergravity (2408.03852v1)

Abstract: We obtain de Sitter (dS) solutions from controlled string-theory constructions. We review how minimal gauged chiral 6D supergravity evades standard dS no-go theorems by having a positive scalar potential and describe the known 4D classical dS, AdS and Minkowski solutions. Grimm and collaborators recently found a related 6D supergravity by direct F-theory Calabi-Yau flux compactifications and we construct classical 4D maximally symmetric solutions for this 6D supergravity. These provide explicit solutions of the higher-dimensional field equations corresponding to dS, AdS and flat spacetimes in 4D, allowing interesting hierarchies of scales. We show how the singularities of these solutions are consistent with the back-reaction of two space-filling 4D brane-like sources situated within the extra dimensions and infer some of the properties of these sources using the formalism of point particle effective field theory (PPEFT), showing the sources are not vanilla objects like D branes. These tools relate the near-source asymptotic forms of bulk fields to source properties and have been extensively tested for more prosaic physical systems involving the back-reaction of small sources, such as the dependence of atomic energy levels on nuclear properties. We use it to determine the tension of the brane-like sources (that can be positive) and its derivatives. We verify that the solutions are in the weak coupling/large volume regime required to neglect quantum and $\alpha'$ effects.

• The paper constructs a framework using 6D gauged supergravity, often derived from string theory setups like F-theory, to find 4D de Sitter, Anti-de Sitter (AdS), and Minkowski solutions.
• Authors present explicit 4D de Sitter solutions by managing extra dimensions and back-reaction of sources, systematically interpreting singularities using Point-Particle Effective Field Theory (PPEFT).
• This research provides a potential pathway for realizing 4D de Sitter universes naturally from string theory, integrating theoretical advances with cosmological observations like dark energy.

4D de Sitter from String Theory via 6D Supergravity

The paper "4D de Sitter from String Theory via 6D Supergravity" by Burgess, Muia, and Quevedo presents an investigation into deriving effective four-dimensional (4D) de Sitter solutions from string theory through an intermediary six-dimensional (6D) supergravity framework. This work addresses several long-standing challenges in string theory, particularly related to de Sitter space and its viable realization within a quantum gravitational setup.

The approach in the paper is structured around overcoming two notable obstacles: classical no-go theorems and the Dine-Seiberg problem. Classical no-go theorems have traditionally highlighted the lack of viable de Sitter solutions within certain supergravity and string frameworks. Specifically, these theorems suggest under a set of assumptions, such solutions are not possible due to the nature of the equations governing the low-energy limit of string theory. Concurrently, the Dine-Seiberg problem emphasizes the potential for scalar fields to cause runaway behavior, precluding stabilization in a vacuum that features maximal symmetry.

To reconcile these challenges, the authors construct a framework primarily utilizing 6D chiral gauged supergravity as derived from string theory setups. Notably, they explore gauged 6D supergravity, such as those obtained from F-theory compactifications on elliptically fibered Calabi-Yau manifolds. Through the conduit of 6D supergravity, they demonstrate the existence of 4D de Sitter, Anti-de Sitter (AdS), and Minkowski solutions, effectively circumventing traditional barriers posed by no-go theorems in higher dimensions.

Key Contributions and Methodologies:

1. Framework and Theoretical Basis: The paper describes a methodical construction of solutions in 6D gauged supergravity, which stem from controlled string theory-derived setups. F-theory provides a compelling basis, leveraging its compactifications that naturally produce the requisite scalar potentials conducive to their analysis.
2. Explicit Solutions: The authors present explicit construction of 4D de Sitter solutions and other maximally symmetric 4D solutions by managing the extra-dimensional configuration and dealing with the implications of back-reaction of codimension-two sources, or branes.
3. Handling Singularities with PPEFT: The authors employ Point-Particle Effective Field Theory (PPEFT) techniques to systematically address and interpret the singularities that arise in the solutions. These singularities signal the presence of gravitating sources necessary for the stabilization within their model. PPEFT provides a framework for estimating source properties, further evidencing the consistency of these solutions with known stringy constituents.
4. Numerical and Asymptotic Analysis: By leveraging both numerical solutions and asymptotic analysis, the authors delineate regions in parameter space where physics varies, including identifying singularities and the behavior of scalar fields across these regimes.

Implications and Future Outlook:

The implications of this research are multifaceted, offering a potential pathway towards realizing 4D de Sitter universes arising naturally from string theoretical frameworks, an outcome historically fraught with complexity. The aligning of de Sitter solutions within a semi-classical context, without substantial reliance on quantum corrections, enhances computational control and reliability. Notably, the solutions promote an invigorating dialogue about reconciling the string landscape with observable cosmological features such as dark energy.

The framework set forth in this paper opens the door for further exploration into time-dependent inflationary solutions derived directly from higher-dimensional theories. Continued work might also explore the specifics of stabilizing these solutions fully within a concrete string model, addressing questions of higher-dimensional geometry and gauge symmetries, along with extending EFT techniques to more complicated brane setups.

In conclusion, by bridging constructs of higher-dimensional supergravity with 4D cosmological models via string theory insights, the paper makes strides in shaping a more coherent picture of de Sitter space within fundamental physics. This work provides a necessary step toward integrating theoretical advances with empirical necessities, further cementing the role of string theory in modern cosmological predictions.