Fermionic un-particles, gauge interactions and the $\beta$ function

TL;DR

This paper develops a theoretical framework for fermionic unparticles, explores their gauge interactions, and analyzes their impact on the beta function, revealing a fermion-like and scalar-like contribution with implications for conformal invariance.

Contribution

It introduces a first-principles approach to fermionic unparticles, formulates a gauge theory for them, and examines their effects on the beta function, highlighting the role of conformal invariance.

Findings

Unparticles can be described as canonically quantized fields with non-local interactions.

Fermionic unparticles contribute to the beta function as a sum of fermion-like and scalar-like terms.

Full conformal invariance causes the scalar-like contribution to vanish.

Abstract

The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We further develop a possible gauge theory for fermionic unparticles. Computing the consequent contribution of un-fermions to the $\beta$ function of the theory, it is shown that this can be viewed as the sum of two contributions, one fermion-like and the other scalar-like. However, if full conformal invariance is imposed, the latter vanishes identically. We discuss the consequences thereof as well as some general phenomenological issues.