D-branes, Cyclic Symmetry and Noncommutative Geometry

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 (${\text{a}}^{\mathrm{\prime }}$-corrections) and the noncommutative geometry (${\mathrm{\Theta }}_A$-corrections) is presented to explain some of the unusual IR phenomena often noticed in a noncommutative theory.