Field Theory On The World Sheet: Crystal Formation

In a previous work, a world sheet field theory which sums planar phi^3 graphs was investigated. In particular, a solitonic solution of this model was constructed, and quantum fluctuations around this solution led to a string picture. However, there were two problems which were not treated satisfactorily: An ultraviolet divergence and a spurious infrared divergence. Here we present an improved treatment, which eliminates the ultraviolet divergence in the normal fashion by mass and coupling constant renormalization. The infrared problem is taken care of by choosing a classical background which forms a one dimensional crystal. The resulting picture is a hybrid model with both string and underlying field theory excitations. Only in the dense graph limit on the world sheet a full string picture emerges.