Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry

Abstract

It is argued that the quadratic and linear non-commutative IR divergences that occur in U(1) theory on non-commutative Minkowski spacetime for small non-commutativity matrices ${\theta }^{\mu \nu }$ are gauge-fixing independent. This implies in particular that the perturbative tachyonic instability produced by the quadratic divergences of this type in the vacuum polarization tensor is not a gauge-fixing artifact. Supersymmetry can be introduced to remove from the renormalized Green functions at one loop, not only the non-logarithmic non-commutative IR divergences, but also all terms proportional to ${\theta }^{\mu \nu }{p}_{\nu }$

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References in corpus (1)

• Noncommutative $\mathcal{N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop

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