Anomalies, Unparticles, and Seiberg Duality

TL;DR

This paper computes triangle anomalies for unfermions with non-canonical scaling, confirming that anomaly factors are independent of scaling dimension and match those of ordinary fermions, supporting unparticle physics in conformal theories.

Contribution

It provides a method to calculate anomalies for unfermions in Seiberg duality, demonstrating their anomaly factors match those of standard fermions regardless of scaling dimension.

Findings

Anomaly factors for unfermions are independent of their scaling dimension.

The calculation parallels the standard fermion case despite complex propagators.

Supports unparticle actions as accurate descriptions of conformal fixed point theories.

Abstract

We calculate triangle anomalies for fermions with non-canonical scaling dimensions. The most well known example of such fermions (aka unfermions) occurs in Seiberg duality where the matching of anomalies (including mesinos with scaling dimensions between 3/2 and 5/2) is a crucial test of duality. By weakly gauging the non-local action for an unfermion, we calculate the one-loop three-current amplitude. Despite the fact that there are more graphs with more complicated propagators and vertices, we find that the calculation can be completed in a way that nearly parallels the usual case. We show that the anomaly factor for fermionic unparticles is independent of the scaling dimension and identical to that for ordinary fermions. This can be viewed as a confirmation that unparticle actions correctly capture the physics of conformal fixed point theories like Banks-Zaks or SUSY QCD.