A First-Quantized Model For Unparticles and Gauge Theories Around Conformal Window

TL;DR

This paper develops a first-quantized model for unparticles and gauge theories near the conformal window, revealing how conformal symmetry and confinement influence the mass spectrum and unparticle behavior.

Contribution

It introduces a unified first-quantized framework that describes both confining and conformal phases, including a tensionless limit where unparticles emerge from confined states.

Findings

The model exhibits Regge trajectories in the confining phase.

A tensionless limit leads to unparticle behavior and conformal symmetry restoration.

Mass ratios remain constant in the high-energy limit.

Abstract

We first quantize the action proposed by Casalbuoni and Gomis in [Phys. Rev. D \textbf{90}, 026001 (2014)], an action that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in terms of an effective string tension $\sigma\,$. The quantized model is confining when $\sigma\neq0$ and its mass spectrum shows Regge trajectories. We propose a tensionless limit in which highly excited confined states reduce to (gapped) unparticles. Moreover, the low-lying confined bound states become massless in the latter limit as a sign of conformal symmetry restoration and the ratio between their masses and $\sqrt\sigma$ stays constant. The originality of our approach is that it applies to both confining and conformal phases via an effective interacting model.