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.

arXiv commentPh.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

References in corpus (61)

• Noncommutative Field Theory
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Noncommutative Field Theory and Lorentz Violation
• Noncommutative Open String and D-brane
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• A Gravity Theory on Noncommutative Spaces
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Space/Time Non-Commutativity and Causality
• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Noncommutative Geometry From Strings and Branes
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• General Properties of Noncommutative Field Theories
• Noncommutative Field Theories and Gravity
• Physical Instances of Noncommuting Coordinates
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Deformed Coordinate Spaces; Derivatives
• A Noncommutative M-Theory Five-brane
• "Peireles Substitution" and Chern-Simons Quantum Mechanics
• Derivative corrections to D-brane actions with constant background fields
• Noncommutative gauge theory for Poisson manifolds
• Chiral Gauge Anomalies on Noncommutative R^4
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Noncommutative Gauge Theory without Lorentz Violation
• Axial Anomaly in Noncommutative QED on R^4
• Anomaly freedom in Seiberg-Witten noncommutative gauge theories
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Deformed Symmetry in Snyder Space and Relativistic Particle Dynamics
• Open membranes in a constant C-field background and noncommutative boundary strings
• Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity
• Derivative corrections to the D-brane Born-Infeld action: non-geodesic embeddings and the Seiberg-Witten map
• Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
• Space-time symmetry of noncommutative field theory
• Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• Non-Commutative Geometry and Twisted Conformal Symmetry
• Space-Time Symmetries of Noncommutative Spaces
• Deformed QED via Seiberg-Witten Map
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
• Aspects of BRST Quantization
• Noncommutative gauge theories and Lorentz symmetry
• Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
• Membranes and Matrix Models
• Maps for currents and anomalies in noncommutative gauge theories
• Deformed Bialgebra of Diffeomorphisms
• Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
• Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings
• Covariant quantization of membrane dynamics
• Membrane and Noncommutativity
• Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory
• Seiberg-Witten maps and commutator anomalies in noncommutative electrodynamics
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
• Canonical analysis of space-time noncommutative theories and gauge symmetries
• On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
• Lorentz invariant nonabelian gauge theory on noncommutative space-time and BRST symmetry