Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories

TL;DR

This paper explores the relationship between higher-dimensional quantum chromodynamics (QCD) and two-dimensional QCD, analyzing the limit of a strip of finite width and its implications for the glueball spectrum and dimensional reduction.

Contribution

It introduces a method to relate 3D QCD observables to 2D QCD behaviors and investigates the non-trivial limit as the width approaches zero, extending the analysis to four dimensions.

Findings

Proves the non-triviality of the L→0 limit in the strip geometry

Calculates the glueball spectrum in the small width limit

Establishes a connection between higher-dimensional and 2D QCD behaviors

Abstract

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.