An Unparticle Example in 2D

TL;DR

This paper explores unparticle physics through a simple 2D quantum field theory, demonstrating a transition from scale-invariant unparticle behavior to free particles at high energies.

Contribution

It introduces a 2D exactly solvable model as an analog for unparticle physics and analyzes the transition between unparticle and free particle regimes.

Findings

Demonstrates unparticle behavior in a 2D model

Shows transition from scale invariance to free particles

Provides insights into unparticle interactions with standard model-like particles

Abstract

We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles.