Can Seiberg-Witten Map Bypass Noncommutative Gauge Theory No-Go Theorem?

TL;DR

This paper investigates whether the Seiberg-Witten map can circumvent the noncommutative gauge theory no-go theorem, concluding that it cannot, thus impacting noncommutative particle physics model building.

Contribution

The paper demonstrates that the Seiberg-Witten map is only consistent for gauge theories that adhere to the noncommutative no-go theorem, limiting its use in bypassing the restrictions.

Findings

Seiberg-Witten map cannot bypass the no-go theorem.

Consistent Seiberg-Witten map requires adherence to the no-go restrictions.

Implications for noncommutative particle physics models.

Abstract

There are strong restrictions on the possible representations and in general on the matter content of gauge theories formulated on noncommutative Moyal spaces, termed as noncommutative gauge theory no-go theorem. According to the no-go theorem \cite{no-go}, matter fields in the noncommutative U(1) gauge theory can only have $\pm 1$ or zero charges and for a generic noncommutative $\prod_{i=1}^n U(N_i)$ gauge theory matter fields can be charged under at most two of the $U(N_i)$ gauge group factors. On the other hand, it has been argued in the literature that, since a noncommutative U(N) gauge theory can be mapped to an ordinary U(N) gauge theory via the Seiberg-Witten map, seemingly it can bypass the no-go theorem. In this note we show that the Seiberg-Witten map \cite{SW} can only be consistently defined and used for the gauge theories which respect the no-go theorem. We discuss the implications of these arguments for the particle physics model building on noncommutative space.