Trouble with space-like noncommutative field theory

TL;DR

This paper argues that space-like noncommutative scalar field theories face fundamental issues at one loop, lacking a well-defined effective action, which questions their renormalizability and suggests exploring supersymmetry and other noncommutativity types.

Contribution

It demonstrates the non-existence of the one-loop effective action for space-like noncommutative scalar fields, highlighting problems with their renormalizability.

Findings

One-loop effective action does not exist for these theories.

Such theories are not renormalizable at one loop.

Supersymmetrization may be necessary to address issues.

Abstract

It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity.