# QCD 3 On The World Sheet

## TL;DR

This paper applies a world sheet approach to 2+1 dimensional QCD, revealing a phase transition, mass generation, and string formation through variational analysis of the ground state.

## Contribution

It introduces a variational method to analyze the ground state of QCD on the world sheet, demonstrating phase transition and string formation in 2+1 dimensions.

## Key findings

- Ground state is a dense set of graphs on the world sheet.
- Energy of the dense graph state is lower than the empty state.
- Finite mass is generated in the originally massless theory.

## Abstract

In this article, we apply the world sheet approach developed in earlier work to QCD in 1+2 dimensions. The starting point is a field theory on the world sheet that reproduces the planar graphs of QCD parametrized by the light cone variables. We study the ground state of this model using a variational approach, and show that it consists of a set of graphs infinitely dense on the world sheet. The energy of this new ground state is lower than that of the empty world sheet, signaling a phase transition. Also, a finite mass is generated in the originally massless theory. Finally, we consider a particular set of time dependent fluctuations about the static ground state configuration, which result in the formation of a string on the world sheet.