Abstract
The present article is the continuation of the earlier work, which used the world sheet representation and the mean field approximation to sum planar graphs in massless ϕ 3 field theory. We improve on the previous work in two respects: a prefactor in the world sheet propagator that had been neglected is now taken into account. In addition, we introduce a non-zero bare mass for the field ϕ. Working with a theory with cutoff and using the mean field approximation, we find that, depending on the range of values of the mass and coupling constant, the model has two phases: a string forming phase and a perturbative field theory phase. We also find the generation of a new degree of freedom, which was not in the model originally. This new degree of freedom can be thought of as the string slope, which is now promoted into a fluctuating dynamical variable. Finally, we show that the introduction of the bare mass makes it possible to renormalize the model.
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