A FirstQuantized Model for Unparticles and Gauge Theories around Conformal Window
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 positiondependent 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 lowlying 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.
 Publication:

Universe
 Pub Date:
 December 2021
 DOI:
 10.3390/universe7120471
 arXiv:
 arXiv:2110.11469
 Bibcode:
 2021Univ....7..471B
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 v2 to be published in Universe (MDPI)