Confining string and its widening inHP1embedding approach

Abstract

Structure of confining string in terms of the topological charge density and the action density is studied in SU (2) Yang-Mills theory on the lattice using HP 1 σ-model embedding approach. We find that the confining flux tube noticeably suppresses both the topological charge and the action densities. Beyond the string formation length the string cross section in terms of these quantities is well described by a Gaussian profile. In both cases the squared string width is found to be a logarithmic function of the string length confirming the Lüscher widening of the chromoelectric string. Characteristic string scales in terms of the topological and action densities are estimated as well.

Width of the flux tube in compact U(1) gauge theory in three dimensions

“…where d − 2 is the number of transverse dimensions along which the flux tube vibrates, σ is the string tension, and R 0 is a parameter with the dimensions of a length. This prediction has been confirmed by numerical simulations in different confining lattice gauge theories (LGTs), both with Abelian [11][12][13][14][15][16][17] and non-Abelian local symmetry [18][19][20][21].…”

Topological density fluctuations and gluon condensate around confining string in Yang–Mills theory

“…The early numerical simulations -which used a cooling procedure in order to push the quantum fields towards a smooth classical limit -have indeed revealed a suppression of the local fluctuations of the topological charge density at the string axis [8,9]. The subsequent study of the topological susceptibility in the uncooled vacuum confirmed the suppression of the topological susceptibility at the string axis [10]. In addition it was observed that as the string gets longer the suppression region widens in the transverse direction with respect to the string axis [10].…”

Inside the SU(3) quark-antiquark QCD flux tube: Screening versus quantum widening

“…The widening as been recently extended with two-loop calculations [47]. So far widening has been verified numerically for compact U(1) QED D = 2 + 1 lattices [48] and for non-abelian SU(2) D = 2 + 1 lattices [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. The widening in SU(3) lattice QCD and in D = 3 + 1, which is the pure gauge closer to real strong interactions, has not been measured previously.…”