Complex Liouville String

We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges c∈13+iR on the world sheet. We compute its amplitudes from first principles and establish a duality with a double-scaled two-matrix integral. We also analyze general world sheet boundaries and nonperturbative effects in the genus expansion. By expressing the complex Liouville string as a 2D dilaton gravity theory with a sine potential, we show that it admits both AdS₂ and dS₂ vacua.