Abstract
We address the effect of a quantum gravity induced minimal length on a physical observable for three-dimensional Yang-Mills. Our calculation is done within stationary perturbation theory. Interestingly enough, we find an ultraviolet finite interaction energy, which contains a regularized logarithmic function and a linear confining potential. This result highlights the role played by the new quantum of length in our discussion.
Highlights
It is known that one of the main unsolved problems in high energy physics is a quantitative description of confinement in quantum chromodynamics (QCD)
Albeit phenomenological models still represent a key tool for understanding confinement physics
In this context we recall the phenomenon of condensation, where in the scenario of dual superconductivity, it is conjectured that the QCD vacuum behaves as a dual-type II superconductor
Summary
It is known that one of the main unsolved problems in high energy physics is a quantitative description (from first principles) of confinement in quantum chromodynamics (QCD). In recent times, a new formulation of non-commutative quantum field theory in the presence of a minimal length has been proposed in [18,19,20]. Afterwards, this approach was further developed by the introduction of a new multiplication rule, which is known as Voros star-product. With the introduction of non-commutativity by means of a minimal length, the theory becomes ultraviolet finite and the cutoff is provided by the non-commutative parameter θ In this perspective the present work is an extension of our previous study [22]. Our study offers a straightforward calculation in which some features of three-dimensional non-Abelian gauge theories become more transparent
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