Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation

Abstract: We show 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. Our 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.