Lambert-W solves the noncommutative $\hat{I}{¦}^4$-model

Abstract

The closed Dyson-Schwinger equation for the 2-point function of the noncommutative $\hat{I}»\ddot{I}{•}_2^4$-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 $\hat{I}»$ inside a domain which contains $(-1/\log 4,\infty )$. Our methods include the Hilbert transform, perturbation series and Lagrange-Bürmann resummation.

LaTeX, 28 pages, 2 figures. v2: main conjecture in v1 is now a theorem