Quantum instability of gauge theories on $\kappa$-Minkowski space

Abstract

We consider a gauge theory on the 5-d $\kappa$-Minkowski which can be viewed as the noncommutative analog of a $U(1)$ gauge theory. We show that the Hermiticity condition obeyed by the gauge potential $A_{\mu }$ is necessarily twisted. Performing a BRST gauge-fixing with a Lorentz-type gauge, we carry out a first exploration of the one loop quantum properties of this gauge theory. We find that the gauge-fixed theory gives rise to a non-vanishing tadpole for the time component of the gauge potential, while there is no non-vanishing tadpole 1-point function for the spatial components of $A_{\mu }$. This signals that the classical vacuum of the theory is not stable against quantum fluctuations. Possible consequences regarding the symmetries of the gauge model and the fate of the tadpole in other gauges of non-covariant type are discussed.

21 pages. Misprints corrected. The discussion has been enlarged as to include the case of "non-covariant" gauges of axial type. Version to appear in Phys. Rev. D

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Cited by in corpus (5)

• Gauge theories on quantum spaces
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Star-products for Lie-algebraic noncommutative Minkowski space-times
• Algebraic structures in $\kappa$-Poincaré invariant gauge theories