Planarity in Noncommutative Gauge Theories

TL;DR

This paper explores the concept of planarity in noncommutative gauge theories, highlighting its origins, how it manifests differently from commutative cases, and its implications in two-dimensional models where explicit calculations are possible.

Contribution

It clarifies the merging of different planarity notions in noncommutative gauge theories and provides explicit computations in two dimensions.

Findings

Planarity in noncommutative theories combines topological and cyclic invariance.

Explicit gauge-invariant correlators are computed in 2D models.

The study reveals intriguing features unique to noncommutative gauge theories.

Abstract

Planarity was introduced by 't Hooft in his topological classification of diagrams in the large-N limit of U(N) gauge theories. Planarity also occurs in noncommutative field theories where amplitudes possess invariance only under cyclic permutations, a feature inherited from the parent string theory. In noncommutative gauge theories both kinds of planarity merge in a context which turns out to be particularly intriguing in the two-dimensional case where gauge invariant correlators can be explicitly computed.