Scalar Field Theories On The World Sheet: A Non-Trivial Ground State

The present article completes an earlier publication, which was the culmination of a series of papers dedicated to the study of the planar graphs of the scalar phi^3 theory on a light cone world sheet. In the earlier work, a field theory on a continuous world sheet that reproduces these planar graphs was constructed, and the mean field approximation was applied to it. This led to the formation of a soliton, and the fluctuations around the soliton were identified with stringy excitations. We point out, however, that in this earlier work, a complete treatment of the ground state of the model was missing. This was due to an unnecessary decompactification of the world sheet; by keeping it compactified, we show that, in addition to a trivial ground state, there is also a non-trivial one. We investigate fluctuations around the non-trivial ground state in the limit of a densely populated world sheet, and show string formation in this limit. We also show that this limit can be systematically studied by means of an expansion in terms of a conveniently defined coupling constant.