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

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, with the temporal dependence, 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.