The Complex Liouville String

I will introduce a new 2d gravity/matrix integral duality. The bulk theory is a two-dimensional string theory defined by coupling two copies of Liouville CFT with central charges c = 13 ± is on the worldsheet. We call this string theory the complex Liouville string. The complex Liouville string may be recast semiclassically in terms of a 2d dilaton gravity with a sine potential for the dilaton. This dilaton gravity theory admits solutions with both signs of the cosmological constant. I will argue that the complex Liouville string admits a dual description in terms of a double-scaled two-matrix integral. Furthermore the string amplitudes, which are the main observables of the complex Liouville string, can be interpreted as the cosmological correlators at future infinity of dS3. This talk is based on work in progress in collaboration with Scott Collier, Lorenz Eberhardt, and Victor Rodriguez.