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Recent no‐go theorems have ruled out four‐dimensional classical de Sitter vacua in heterotic string theory. On the other hand, the absence of a well‐defined Wilsonian effective action and other related phenomena also appear to rule out such time‐dependent vacua with de Sitter isometries, even in the presence of quantum corrections. In this note, the authors argued that a four‐dimensional de Sitter space can still exist in SO(32)$SO(32)$ heterotic string theory as a Glauber–Sudarshan state, i.e., as an excited state, over a supersymmetric Minkowski background, albeit within a finite temporal domain. Borel resummation and resurgence play a crucial role in constructing such a state in the Hilbert space of heterotic theory governed entirely by the IR degrees of freedom. [ABSTRACT FROM AUTHOR]

It is shown in this article that an explicit construction of a four‐dimensional de Sitter space may be performed using a diagrammatic approach via nodal diagrams emanating from the path integral representation of the Glauber‐Sudarshan state. Sum of these diagrams typically leads to an asymptotic series of Gevrey kind which can then be Borel resummed, thus reproducing the non‐perturbative structure of the system. The analysis shows that four‐dimensional de Sitter space is not only possible in string theory overcoming the no‐go and the swampland criteria—albeit as a Glauber‐Sudarshan state—but it may also be non‐perturbatively stable within a controlled temporal domain. Somewhat consistently, the Borel resummation of the Gevrey series provides strong hint towards the positivity of the cosmological constant. [ABSTRACT FROM AUTHOR]

We provide further evidence to support the fact that a four‐dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no‐go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber‐Sudarshan state. We show here that this result is independent of the choice of de Sitter slicings. The Glauber‐Sudarshan state, constructed by shifting the interacting vacuum in the M‐theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger‐Dyson's equations in the presence of hierarchically controlled perturbative and non‐perturbative quantum corrections. Additionally, we provide a detailed study of the fluxes supporting the Glauber‐Sudarshan state in the M‐theory uplift of the IIB scenario. We show explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along‐with the constraints from the Schwinger‐Dyson's equations, conspire together to provide the necessary temporal dependences to support such a state in full M‐theory. We also discuss how our analysis points towards a surprising connection to the four‐dimensional null energy condition, for a Friedman‐Lemaitre‐Robertson‐Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M‐theory. The authors provide further evidence to support the fact that a four‐dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no‐go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber‐Sudarshan state. It is shown here that this result is independent of the choice of de Sitter slicings. The Glauber‐Sudarshan state, constructed by shifting the interacting vacuum in the M‐theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger‐Dyson's equations in the presence of hierarchically controlled perturbative and non‐perturbative quantum corrections. Additionally, a detailed study of the fluxes supporting the Glauber‐Sudarshan state in the M‐theory uplift of the IIB scenario will be provided. It will be shown explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along‐with the constraintsfrom the Schwinger‐Dyson's equations, conspire together to provide the necessary temporaldependences to support such a state in full M‐theory. There will be a discussion how the analysis given here points towards a surprising connection to the four‐dimensional null energy condition, for a Friedman‐Lemaitre‐Robertson‐Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M‐theory. [ABSTRACT FROM AUTHOR]