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

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 arXiv:2511.03798 [hep-th].

72 pages, 14 figures, Companion paper