Remarks on the interquark potential in the presence of a minimal length

Abstract

Abstract. We calculate the lowest-order corrections to the static potential for both Yang-Mills theory and gluodynamics in curved space-time, in the presence of a quantum gravity induced minimal length. Our analysis is carried out within stationary perturbation theory. As a consequence, the potential energy is the sum of a Yukawalike potential and a linear potential for gluodynamics in curved space-time, leading to the confinement of static charges. Interestingly enough, we obtain that the coefficient of the linear term ("string tension") is ultraviolet finite. We should highlight the role played by the new quantum of length in our analysis.

On Finite Interquark Potential inD=3Driven by a Minimal Length

“…In this perspective the present work is an extension of our previous study [22]. Thus, the basic ideas underlying the analysis of this paper are derived from our earlier paper [22]. Specifically, in this work we will focus attention on the impact of a minimal length on a physical observable for pure Yang-Mills theory in (2 + 1)D. It is worthy noting here that Yang-Mills theories in (2 + 1)D are very relevant for a reliable comparison between results coming from continuum and lattice calculations [23].…”

“…To conclude, let us put our work in its proper perspective. As already anticipated, this work is a sequel to [22], where we have considered a three-dimensional extension of the recently (3 + 1)D calculation in the presence of a minimal length. To do this, we have exploited a correct identification of field degrees with observable quantities.…”

“…In this perspective the present work is an extension of our previous study [22]. Thus, the basic ideas underlying the analysis of this paper are derived from our earlier paper [22].…”

“…Following our earlier procedure, the corresponding formulation of this theory in the presence of a minimal length is by means of a smeared source [22,31,32]. Thus, we will take the sources as ρ a ≡ ρ a…”

“…ν , with f abc the structure constants of the gauge group. As we have indicated in [22], our analysis is based in perturbation theory along the lines of Refs. [28][29][30].…”