Towards the Realistic Gluodynamics String. Perturbative Gluons' Contribution to the String Effective Action

TL;DR

This paper derives a correction to the string effective action in nonperturbative QCD by considering perturbative gluon interactions, revealing that these interactions modify the rigidity term but not the string tension.

Contribution

It introduces a novel perturbative correction to the string effective action in SU(2) gluodynamics, highlighting the spin-dependent effects on the rigidity term.

Findings

Interaction affects only the rigidity term's coupling constant

The correction depends on the Wilson loop's representation spin

The string tension remains unaffected by the perturbative gluons

Abstract

Perturbation theory in the nonperturbative QCD vacuum and the non-Abelian Stokes theorem, representing a Wilson loop in the SU(2) gluodynamics as an integral over all the orientations in colour space, are applied to derivation of the correction to the background-induced string effective action. This correction is due to accounting in the lowest order of perturbation theory for the interaction of perturbative gluons with the string world sheet. It occurs that this interaction affects only the coupling constant of the rigidity term, while its contribution to the string tension of the Nambu-Goto term vanishes. The obtained correction to the rigid string coupling constant multiplicatively depends on the spin of the representation of the Wilson loop under consideration, the QCD coupling constant and a certain path integral, which includes the background Wilson average.