A Computational Companion to Transient de Sitter and Quasi de Sitter States in SO(32) and E_8 X E_8 Heterotic String Theories I: Formalisms

TL;DR

This work advances a framework in which four-dimensional de Sitter space is realized not as a vacuum, but as an excited Glauber-Sudarshan state over a Minkowski background, enabling de Sitter isometries in type IIB and heterotic theories via dynamical M-theory dualities. A detailed path-integral analysis in M-theory, including all-order perturbation theory and non-perturbative resummation via Borel-Écalle methods, yields a finite, trans-series description for the metric expectation value and connects EFT viability to the Null Energy Condition. The study also clarifies how trans-horizon and axion cosmology constraints shape warp-factor scalings, the Trans-Planckian Censorship Conjecture bound, and the time dependence of axion couplings in E8xE8 heterotic theory. Together these results provide a concrete computational companion to the intermediate steps in the corresponding longer work, and offer a controlled path to realizing transient de Sitter-like phases within foundational string-theoretic settings.

Abstract

We construct four-dimensional de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic SO(32), and heterotic E_8 \times E_8 string theories. This framework provides a mechanism to evade vacuum-based no-go theorems for de Sitter solutions in string theory. Starting from a generic M-theory configuration, we obtain de Sitter isometry in the dual string theories through appropriate dynamical duality sequences in the late-time limit. The excited state, identified as a Glauber-Sudarshan state, is constructed as the expectation value of the metric operator in M-theory using path-integral techniques. We further analyze the conditions required for the existence of a well-defined effective field theory description and show that these conditions are equivalent to the Null Energy Condition for a (3+1)-dimensional FLRW cosmology. Finally, we investigate constraints arising from axionic cosmology and demonstrate how the time-dependent solutions are modified when experimental bounds on the axionic coupling constant are taken into account. This article serves as a computational companion to sections 3 and 4 of the paper https://doi.org/10.48550/arXiv.2511.03798.

Figures (12)

• Figure 1: The region of embedding space $d\mathrm{S}^d$ covered by the poincare coordinates $\mathrm{X}^0\geq -\mathrm{X}^d$ (shown using dashed lines), the constant $\mathrm{X}^0$ slices are $\mathrm{S}^{d-1}$.
• Figure 2: Duality sequence to go from the $\mathrm{M}$ theory configuration (\ref{['MthEorYmeTric']}) to type $\mathrm{IIB}$ string theory (\ref{['tyPeIIBMetrIc']}) having de Sitter isometry. Here $\mathcal{G}$ denotes some group action without any fixed points.
• Figure 3: Duality sequence to go from the $\mathrm{M}$ theory configuration (\ref{['MthEorYmeTric']}) to heterotic $\mathrm{SO(32)}$ string theory (\ref{['HeTerotiCSO(32)MetrIc']})
• Figure 4: Duality sequence to go from the $\mathrm{M}$ theory configuration (\ref{['MthEorYmeTric']}) to heterotic $\mathrm{E_8}\times\mathrm{E}_8$ string theory (\ref{['DiffDSE8']}) with the gauge group broken down to $(SO(8))^4$
• Figure 5: Duality sequence to go from the $\mathrm{M}$ theory configuration (\ref{['MthThreewarpFac']}) to heterotic $\mathrm{E}_{8}\times \mathrm{E}_{8}$ string theory (\ref{['HetroTicE8XE8 metric']})