Further Results about Field Theory on the World Sheet and String Formation

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 phi^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 phi. 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. The 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.

39 pages, 10 figures, typos corrected and one equation simplified

References in corpus (2)

• Renormalization of Quantum Fields on the Lightcone Worldsheet I: Scalar Fields
• Meanfield Approximation For Field Theories On The Worldsheet Revisited

Cited by in corpus (6)

• On the worldsheet theories of strings dual to free large N gauge theories
• Comments on worldsheet theories dual to free large N gauge theories
• On a worldsheet dual of the Gaussian matrix model
• From Spacetime to Worldsheet: Four point correlators
• Mean Field Method Applied To The New World Sheet Field Theory: String Formation
• Summing Planar Bosonic Strings