The Gauge Anomaly and the Seiberg-Witten Map

Abstract

The consistent form of the gauge anomaly is worked out at first order in $\theta$ for the noncommutative three-point function of the ordinary gauge field of certain noncommutative chiral gauge theories defined by means of the Seiberg-Witten map. We obtain that for any compact simple Lie group the anomaly cancellation condition of this three-point function reads $\traza \T^a \T^b \T^c = 0$, if one restricts the type of noncommutative counterterms that can be added to the classical action to restore the gauge symmetry to those which are renormalizable by power-counting. On the other hand, if the power-counting remormalizability paradigm is relinquished and one admits noncommutative counterterms (of the gauge fields, its derivatives and $\theta$) which are not power-counting renormalizable, then, the anomaly cancellation condition for the noncommutative three-point function of the ordinary gauge field becomes the ordinary one: $\traza \T^a \{\T^b,\T^c\} = 0$.

26 pages, 1 figure. A reference has been added

References in corpus (4)

• Non-renormalizability of θ-expanded noncommutative QED
• Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
• Towards an explicit expression of the Seiberg-Witten map at all orders
• Noncommutative 1-cocycle in the Seiberg-Witten map

Cited by in corpus (44)

• The Z -> gamma gamma, gg Decays in the Noncommutative Standard Model
• The photon-neutrino interaction in non-commutative gauge field theory and astrophysical bounds
• Probing the Noncommutative Standard Model at Hadron Colliders
• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Anomaly freedom in Seiberg-Witten noncommutative gauge theories
• The one-loop renormalization of the gauge sector in the noncommutative standard model
• The Noncommutative Standard Model at O(theta^2)
• What are the Bounds on Space-Time Noncommutativity?
• Spacetime noncommutativity and ultra-high energy cosmic ray experiments
• The absence of the 4$\psi$ divergence in noncommutative chiral models
• Effective Field Theories on Non-Commutative Space-Time
• Constraining spacetime noncommutativity with primordial nucleosynthesis
• Semi-Leptonic Decay of a Polarized Top Quark in the Noncommutative Standard Model
• Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory
• Computing the θ-exact Seiberg-Witten map for arbitrary gauge groups
• Photon-neutrino interaction in theta-exact covariant noncommutative field theory
• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion
• On UV/IR mixing in noncommutative gauge field theories
• Neutrino propagation in noncommutative spacetimes
• Self-energies on deformed spacetimes
• Noncommutative fermions and quarkonia decays
• AdS-inspired noncommutative gravity on the Moyal plane
• Particle phenomenology on noncommutative spacetime
• Quantum Electrodynamics on Noncommutative Spacetime
• Singlet particles as cold dark matter in noncommutative space-time
• Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings
• Remarks on the 2nd order Seiberg-Witten maps
• Seiberg-Witten map Invariant Scatterings
• Yukawa terms in noncommutative SO(10) and E6 GUTs
• TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams
• Single top quark production in $t$-channel at the LHC in Noncommutative Space-Time
• Noncommutative Standard Model in Top Quark Sector
• SO(10) GUTs with large tensor representations on Noncommutative Space-time
• The Minimal and the New Minimal Supersymmetric Grand Unified Theories on Noncommutative Space-time
• Two-Point Functions on Deformed Spacetime
• Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• The U(1)A anomaly in noncommutative SU(N) theories
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories
• Laboratory frame analysis of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering in the Noncommutative Standard Model
• Revisiting NCQED and scattering amplitudes
• The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions