Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing

TL;DR

This paper investigates light-like noncommutative field theories using light-front quantization, revealing that UV/IR mixing persists despite initial indications it might be absent, and supports their perturbative unitarity.

Contribution

It demonstrates that UV/IR mixing remains in light-like noncommutative theories when quantized via light-front methods, challenging previous assumptions based on covariant quantization.

Findings

UV/IR mixing persists in light-like noncommutative theories.

Light-front quantization reveals UV cutoff as IR cutoff for p^+.

Supports perturbative unitarity of these theories.

Abstract

We revisit the problem of quantizing field theories on noncommutative Moyal spacetime with \emph{light-like} noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, $p^+$. Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.