The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics

Abstract

It has been conjectured in the literature that renormalizability of the $\theta$-expanded noncommutative gauge theories improves when one takes into account full nonuniqueness of the Seiberg-Witten expansion, which relates noncommutative (`high-energy') with commutative (`low-energy') fields. In order to check this conjecture we analyze renormalizability of the noncommutative chiral electrodynamics: we quantize the action which contains all possible terms implied by the SW map. After renormalization we arrive at a different theory in which the relation between the coupling constants is changed. This means that the $\theta$-expanded chiral electrodynamics is not renormalizable: when fermions are included, the SW expansion is not preserved in quantization.

16 pages

References in corpus (5)

• Seiberg--Witten Maps to All Orders
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Non-commutative SU(N) gauge theories and asymptotic freedom
• The absence of the 4$\psi$ divergence in noncommutative chiral models
• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion

Cited by in corpus (2)

• Self-energies on deformed spacetimes
• Two-Point Functions on Deformed Spacetime