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 space-time 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).