Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
arXiv:0711.3059 · doi:10.1103/PhysRevD.77.045033
Abstract
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar phi^4 braided noncommutative field theory in Lie-algebraic noncommutative spacetime, [x^i,x^j]=2i kappa epsilon^{ijk}x_k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter kappa. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry.
arXiv comment20 pages, no figures, references added
References in corpus (54)
- String Theory and Noncommutative Geometry
- The quantum structure of spacetime at the Planck scale and quantum fields
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Noncommutative Perturbative Dynamics
- Gauge Theory on Noncommutative Spaces
- 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
- Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
- Noncommutative Solitons
- Noncommutative Geometry and Gravity
- Space/Time Non-Commutativity and Causality
- Perturbative analysis on infrared aspects of noncommutative QED on R^4
- Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
- New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
- Solitons in Noncommutative Gauge Theory
- Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
- Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
- Flux tube solutions in noncommutative gauge theories
- Dynamics of Strings in Noncommutative Gauge Theory
- Deformed Coordinate Spaces; Derivatives
- Noncommutative Multi-Solitons in 2+1 Dimensions
- Instantons on Noncommutative R^4 and Projection Operators
- Monopoles and Strings in Noncommutative Gauge Theory
- Statistics and UV-IR Mixing with Twisted Poincare Invariance
- On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
- Remarks on Time-Space Noncommutative Field Theories
- Exact Solutions of Multi-Vortices and False Vacuum Bubbles in Noncommutative Abelian-Higgs Theories
- Nielsen-Olesen Vortices in Noncommutative Abelian Higgs Model
- A note on the noncommutative correction to gravity
- UV-IR Mixing in Non-Commutative Plane
- Unstable Solitons in Noncommutative Gauge Theory
- Lie algebraic Noncommutative Gravity
- Construction of -Poincaré Algebras and their Invariants on
- Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
- Braided Quantum Field Theory
- Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
- Remarks on twisted noncommutative quantum field theory
- Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
- Notes on Noncommutative Instantons
- Noncommutative Solitons: Moduli Spaces, Quantization, Finite Theta Effects and Stability
- Dp-D(p+4) in Noncommutative Yang-Mills
- ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories
- Braided quantum field theories and their symmetries
- Noncommutative Field Theory from twisted Fock space
- Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
- Scalar field theories in a Lorentz-invariant three-dimensional noncommutative space-time
- Drinfeld Twist and General Relativity with Fuzzy Spaces
- Space-time uncertainty relation and Lorentz invariance
- An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
- The Existence and Stability of Noncommutative Scalar Solitons
- QFT with Twisted Poincaré Invariance and the Moyal Product
- Duality and Braiding in Twisted Quantum Field Theory
- Noncommutative Quantization for Noncommutative Field Theory
Cited by in corpus (6)
- Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
- Poisson structure on a space with linear SU(2) fuzziness
- The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
- Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions
- Massive particles coupled with 2+1 dimensional gravity and noncommutative field theory
- Eigenvalue problem for radial potentials in space with SU(2) fuzziness