Lambert-W Solves the Noncommutative Φ4-Model

The closed Dyson-Schwinger equation for the 2-point function of the noncommutative λ ϕ₂⁴ -model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution in terms of Lambert's W-function. This solution is holomorphic in λ inside a domain which contains (-1 /log4 ,∞ ) . Our methods include the Hilbert transform, perturbation series and Lagrange-Bürmann resummation.