Aspects of noncommutativity in field theory, strings and membranes

TL;DR

This paper explores the implications of noncommutativity in field theories, strings, and membranes, revealing boundary coordinate algebra, deriving Seiberg-Witten maps, analyzing anomalies, and examining Lorentz invariance in noncommutative gauge theories.

Contribution

It provides new insights into noncommutative structures in various physical theories, including boundary dynamics, anomaly structures, and symmetry properties.

Findings

Boundary string coordinates exhibit noncommutative algebraic features.

Seiberg-Witten maps relate noncommutative and commutative gauge theories.

Explicit criteria for Lorentz invariance preservation in noncommutative theories.

Abstract

We study certain aspects of noncommutativity in field theory, strings and membranes. We analyse the dynamics of an open membrane whose boundary is attached to p-branes. Noncommutative features of the boundary string coordinates are revealed by algebraic consistency arguments. Next, we derive Seiberg-Witten-type maps relating currents and their divergences in nonabelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. We then exploit these maps to obtain the O(\theta) structure of the commutator anomalies in noncommutative electrodynamics. Finally, we discuss the issue of violation of Lorentz invariance in noncommutative gauge theories by explicitly deriving, following a Noether-like approach, the criteria for preserving Poincare invariance. We also study general (deformed) conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces.