D-branes, Cyclic Symmetry and Noncommutative Geometry

TL;DR

This paper explores how cyclic symmetry in open string modes on D p-branes under magnetic fields leads to noncommutative geometry, affecting UV behavior and IR phenomena, with non-perturbative corrections playing a key role.

Contribution

It introduces a novel connection between cyclic symmetry corrections and noncommutative geometry, revealing non-perturbative effects on D p-brane world-volume.

Findings

Constant coordinate modes receive non-perturbative corrections.

Noncommutativity on the D p-brane world-volume is established.

The theory becomes UV-renormalizable and explains IR phenomena.

Abstract

We investigate the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in presence of a magnetic field. It is argued that the constant coordinate modes receive non-perturbative correction. We show that they introduce the notion of noncommutativity on the D p-brane world-volume and make it UV-renormalizable. An analogy between cyclic symmetry ($\a'$-corrections) and the noncommutative geometry ($\Theta_A$-corrections) is presented to explain some of the unusual IR phenomena often noticed in a noncommutative theory.