Aspects of noncommutativity in field theory, strings and membranes

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(θ) 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.

Ph.D. thesis (arXiv version). 132 pages, including front matter. Supervisor: Rabin Banerjee. Institution: S.N. Bose National Centre for Basic Sciences, Kolkata, India. Defended on 29 July 2008 at Jadavpur University, Kolkata, India