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

TL;DR

This paper demonstrates that certain IR divergences in non-commutative U(1) gauge theory are gauge-fixing independent, and shows how supersymmetry can eliminate these divergences and related instabilities at one loop.

Contribution

It establishes gauge-fixing independence of IR divergences and introduces supersymmetry as a means to remove these divergences and tachyonic instabilities.

Findings

IR divergences are gauge-fixing independent

Supersymmetry removes IR divergences at one loop

Supersymmetry eliminates tachyonic instabilities

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 $\theta^{\mu\nu}p_\nu$