A New World Sheet Field Theory

TL;DR

This paper develops a second quantized world sheet field theory for phi^3 planar graphs, demonstrating renormalization and graph condensate formation, advancing the understanding of non-perturbative structures in quantum field theory.

Contribution

It introduces a second quantized approach to world sheet field theory for phi^3 graphs, differing from previous first quantization methods, and analyzes the ground state with renormalization.

Findings

Infinities are renormalized consistently with perturbation theory.

Graphs form a dense condensate on the world sheet in the ground state.

The second quantized formulation aligns with standard perturbative results.

Abstract

A second quantized field theory on the world sheet is developed for summing planar graphs of the phi^3 theory. This is in contrast to the earlier work, which was based on first quantization. The ground state of the model is investigated with the help of a variational ansatz. In complete agreement with standard perturbation theory, the infinities encountered in carrying out this calculation can be eliminated by the renormalization of the parameters of the model. We also find that, as in the earlier work, in the ground state, graphs form a dense network (condensate) on the world sheet.