Field Theory On the World Sheet: Mean Field Expansion And Cutoff Dependence

TL;DR

This paper applies the mean field method to a world sheet field theory, demonstrating how cutoff dependence can be absorbed into a running coupling constant that diminishes in the infrared, leading the model towards a free string.

Contribution

It extends previous work by analyzing higher order terms and their cutoff dependence, showing the coupling constant's behavior and the approach towards a free string in the high energy limit.

Findings

Cutoff dependence absorbed into a running coupling constant

Coupling constant decreases towards zero in the infrared

Model approaches a free string at high energies

Abstract

Continuing earlier work, we apply the mean field method to the world sheet representation of a simple field theory. In particular, we study the higher order terms in the mean field expansion, and show that their cutoff dependence can be absorbed into a running coupling constant. The coupling constant runs towards zero in the infrared, and the model tends towards a free string. One cannot fully reach this limit because of infrared problems, however, one can still apply the mean field method to the high energy limit (high mass states) of the string.