Transient de Sitter and Quasi de Sitter States in SO(32) and E_8 x E_8 Heterotic String Theories

TL;DR

The paper addresses the long-standing challenge of embedding four-dimensional de Sitter and quasi-de Sitter phases in heterotic string theories. It develops a trans-series, resurgent framework in which late-time de Sitter states arise as metastable Glauber-Sudarshan excitations of a Minkowski background, controlled by perturbative and non-perturbative corrections that are organized via a dynamical clock $g_s$ and an emergent dark-energy sector $\Lambda(t)$. Key technical innovations include Weyl-resummed path integrals with wormhole dressing that induce bilocal couplings, a detailed Schwinger-Dyson analysis ensuring IR consistency, and a duality web connecting M-theory uplifts to Type IIB and heterotic theories, all while respecting flux quantization, Bianchi identities, and anomaly cancellation. The framework yields a small positive cosmological constant with possible mild time dependence, and provides a mechanism to embed four-dimensional Standard Model degrees of freedom in a realistic gravitational background with positive dark energy. The results unify perturbative and non-perturbative corrections within a controlled EFT setting, offering a concrete string-theoretic realization of dynamical dark energy and its cosmological implications. The work thus offers a viable path to reconcile string theory with observed late-time acceleration while maintaining theoretical consistency across dual frames and non-perturbative sectors.

Abstract

One of the long-standing puzzles in string theory has been on the existence of a four-dimensional de Sitter and quasi de Sitter configurations, the latter being defined with a temporally varying dark energy, in E_8 x E_8 and SO(32) heterotic theories. In this work, novel dynamical duality-sequences are devised that provide natural constructions of de Sitter and quasi de Sitter excited states in the aforementioned theories allowing no late-time singularities. The emergent positive dark energies -- including the intriguing possibility of their slow temporal variations -- appear from Borel resumming Gevrey series from the path-integral representations of such states. Additionally, precise ways to handle the equations of motion, Bianchi identities, flux quantizations and anomaly cancellations -- consistent with the underlying axionic cosmology and with the probability of forming wormholes that connect baby universes -- are presented for the SO(32) and the E_8 x E_8 theories within a framework that systematically incorporates perturbative and non-perturbative corrections in the far infrared. The temporally varying dark energy, which is much more natural in our set-up because of its emergent nature, surprisingly simplifies many of the aforementioned computations. Interestingly, our analysis also provides, probably for the first time, a set-up to consistently embed four-dimensional standard model degrees of freedom at late time in a realistic gravitational background with positive dark energy from string theory.

Figures (50)

• Figure 1: Wick rotation from $d{\bf S}_2 \subset {\bf R}^{1,2}$ with isometry group $SO(1,2)$ to ${\bf S}^2 \subset {\bf R}^3$ with compact isometry group $SO(3)$.
• Figure 2: A representation of a baby universe appearing from a Minkowski spacetime with a wormhole throat connecting them.
• Figure 3: Simple diagram to illustrate how the trans-series action in a given universe is effected by the presence of a baby universe. Note that it is the wormhole that is responsible for the dressing of the total action.
• Figure 4: The three decay wedges (where ${\rm Re}~{\rm S} > 0$) for the Airy cubic ${\rm S}(z)={z^3\over 3}$. The shaded $60^\circ$ sectors are centered at $\theta=0$ and $\theta = \pm {2\pi\over 3}$; any admissible steepest–descent contour must approach infinity inside two such wedges.
• Figure 5: The plot of ${\rm F}_1(t) = \left(\Lambda t^2\right)^{\beta_o\over 2 - \beta_o}$ for $-1 \le t \le 0$, $\Lambda \equiv 1$ and $0 < \beta_o \equiv y \le {2\over 3}$ in the string frame. For small values of $t$, for example $\epsilon < t < 0$ with $\epsilon$ as in \ref{['tegtrex']}, one may control the behavior of ${\rm F}_1(t)$ using \ref{['evalike']} thus avoiding the late-time singularity of ${\cal M}_4$ in the Einstein frame.