On the Equivalence of Noncommutative Models in Various Dimensions and Brane Condensation

TL;DR

This paper constructs a mathematical map demonstrating the equivalence of noncommutative U(1) Yang-Mills models across different even dimensions, illustrating how D1-branes can condense into higher-dimensional branes.

Contribution

It introduces a novel map linking two-dimensional noncommutative gauge theories with higher-dimensional models, establishing their equivalence and physical interpretation as brane condensation.

Findings

Proved the equivalence of noncommutative models in various even dimensions.

Mapped 2D noncommutative U(1) Yang-Mills fields to D-dimensional models.

Described the physical process of D1-brane condensation.

Abstract

Here we construct a map from the algebra of fields in two-dimensional noncommutative of U(1) Yang-Mills fields interacting with Kaluza-Klein scalars to a D-dimensional one, as a solution in the two-dimensional model. This proves the equivalence of noncommutative models in various (even) dimensions. Physically this map describes condensation of D1-branes.