The epsilon expansion meets semiclassics

We study the scaling dimension Delta(phi n) of the operator phi(n) where phi is the fundamental complex field of the U(1) model at the Wilson-Fisher fixed point in d = 4 - epsilon. Even for a perturbatively small fixed point coupling lambda*, standard perturbation theory breaks down for sufficiently large lambdan. Treating lambdan as fixed for small lambda* we show that Delta(phi n) can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in Delta(phi n) = 1/lambdaDelta(-1)(lambdan)+Delta(0)(lambdan)+lambdaDelta(1)(lambda*n)+ ...