Duality in Scalar Field Theory on Noncommutative Phase Spaces

Abstract

We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined with a star-product, of that which arises in quantum field theories of non-interacting scalar particles coupled to a constant background electromagnetic field. The dual models are in general of the same original form but with transformed coupling parameters, while in certain special cases all parameters are essentially unchanged. Using a particular regualarization we show, to all orders of perturbation theory, that that this duality also persists at the quantum level. We also point out various other properties of this class of noncommutative field theories.

13 pages LaTeX; Minor corrections, references added, comment about self-dual models added to section 4

References in corpus (7)

• Noncommutative Field Theory
• Quantum Hall states as matrix Chern-Simons theory
• Two phases of the noncommutative quantum mechanics
• Quantum Mechanics on the Noncommutative Torus
• Quantum Hall Physics = Noncommutative Field Theory
• Orbital Magnetism of Two-Dimension Noncommutative Confined System
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory

Cited by in corpus (127)

• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Power-counting theorem for non-local matrix models and renormalisation
• Noncommutative Induced Gauge Theory
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Non-commutative Renormalization
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Noncommutative D=4 gravity coupled to fermions
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• Constructive Matrix Theory
• Renormalisation of ϕ^4-theory on noncommutative R^4 to all orders
• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Parametric Representation of Noncommutative Field Theory
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
• Closed equations of the two-point functions for tensorial group field theory
• On the vacuum states for noncommutative gauge theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Renormalization of the noncommutative phi^3 model through the Kontsevich model
• Progress in solving a noncommutative quantum field theory in four dimensions
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Noncommutative epsilon-graded connections
• Geometry of the Grosse-Wulkenhaar Model
• Noncommutative geometry, gauge theory and renormalization
• Probing noncommutative theories with quantum optical experiments
• Gauge theories on quantum spaces
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Propagators for Noncommutative Field Theories
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Galilean symmetry in noncommutative field theory
• New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere
• Noncommutative QFT and Renormalization
• Lectures on Matrix Field Theory I
• Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
• Duality covariant quantum field theory on noncommutative Minkowski space
• Gauge Theories on Deformed Spaces
• The full Ward-Takahashi Identity for colored tensor models
• Noncommutative Induced Gauge Theories on Moyal Spaces
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
• A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Functional Renormalization of Noncommutative Scalar Field Theory
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Symmetries of noncommutative scalar field theory
• Solution of the self-dual ${\Phi }^4$ QFT-model on four-dimensional Moyal space
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Wilsonian Renormalization of Noncommutative Scalar Field Theory
• From scalar fields on quantum spaces to blobbed topological recursion
• Noncommutative U(1) gauge theory from a worldline perspective
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• On space-time noncommutative theories at finite temperature
• Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Duality and Braiding in Twisted Quantum Field Theory
• Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential
• Gauge fields on noncommutative geometries with curvature
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Short Distance Physics and Initial State Effects on the CMB Power Spectrum
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Renormalization on noncommutative torus
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• A Review of Noncommutative Field Theories
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• UV/IR duality in noncommutative quantum field theory
• Nilpotent noncommutativity and renormalization
• Aspects of perturbative quantum field theory on non-commutative spaces
• Twisted Grosse-Wulkenhaar ${\varphi }^{\star 4}$ model: dynamical noncommutativity and Noether currents
• Complete solution of the LSZ Model via Topological Recursion
• On the Effective Action of Noncommutative Yang-Mills Theory
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• Translation-Invariant Noncommutative Renormalization
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Exactly solvable models for 2D correlated fermions
• Matrix Field Theory
• Matrix Model Fixed Point of Noncommutative Phi-Four
• Why Renormalizable NonCommutative Quantum Field Theories?
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Strong Field, Noncommutative QED
• Quantum field theory on projective modules
• Symmetries of field theories on the non-commutative plane
• Quantization of a gauge theory on a curved noncommutative space
• Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Fuzzy Scalar Field Theories: Numerical and Analytical Investigations
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model
• One-loop effects in a self-dual planar noncommutative theory
• Nonlocal regularisation of noncommutative field theories
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Noncommutative Supergeometry and Quantum Supergroups
• Effective Field Theory of a Locally Noncommutative Space-Time and Extra Dimensions
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Relativistic Corrections to the Moyal-Weyl Spacetime
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Induced Gauge Theory on a Noncommutative Space
• Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling
• Constructive Renormalization of the 2-dimensional Grosse-Wulkenhaar Model with Multiscale Loop Vertex Expansions
• Vulcanized Vortex
• A numerical approach to harmonic non-commutative spectral field theory
• Noncommutative real scalar field theory in 2+1 dimensions at finite temperature
• The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples
• Partition function methods for the quartic scalar quantum field theory on the Moyal plane
• Dirichlet boundary conditions in a noncommutative theory
• Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory
• Non-commutative geometry and exactly solvable systems
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory