Comments on the renormalizability of the Broken Phase in Noncommutative Scalar Field Theory

TL;DR

This paper proves the one-loop renormalizability of a noncommutative scalar field theory with spontaneous symmetry breaking, ensuring consistency with Ward identities without specific field ordering.

Contribution

It demonstrates the renormalizability of noncommutative $^4$ theory with broken symmetry at one loop without ordering ambiguities, using a consistent divergence regulation.

Findings

Renormalizability established at one loop

No need for specific field ordering in interactions

Ultraviolet and infrared divergences regulated consistently

Abstract

We study the noncommutative $\phi^4$ theory with spontaneously broken global O(2) symmetry in 4 dimensions. We demonstrate the renormalizability at one loop. This does not require any choice of ordering of the fields in the interaction terms. It involves regulating the ultraviolet and infrared divergences in a manner consistent with the Ward identities.