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We have observed the formation of gluon flux-tubes within baryons usinglattice QCD techniques. A high-statistics approach, based on translational androtational symmetries of the four-dimensional lattice, enables us to observecorrelations between vacuum action density and quark positions in a completelygauge independent manner. This contrasts with earlier studies which usedgauge-dependent smoothing techniques. We used 200 O(a^2) improved quenched QCDgauge-field configurations on a 16^3x32 lattice with a lattice spacing of 0.123fm. In the presence of static quarks flux tubes representing the suppression ofgluon-field fluctuations are observed. We have analyzed 11 L-shapes and 8 T andY shapes of varying sizes in order to explore a variety of flux-tubetopologies, including the ground state. At large separations, Y-shape flux-tubeformation is observed. T-shaped paths are observed to relax towards a Y-shapedtopology, whereas L-shaped paths give rise to a large potential energy. We donot find any evidence for the formation of a Delta-shaped flux-tube (emptytriangle) distribution. However, at small quark separations, we observe anexpulsion of gluon-field fluctuations in the shape of a filled triangle withmaximal expulsion at the centre of the triangle. Having identified the precisegeometry of the flux distribution, we are able to perform quantitativecomparison between the length of the flux-tube and the associated static quarkpotential. For every source configuration considered we find a universal stringtension, and conclude that, for large quark separations, the ground statepotential is that which minimizes the length of the flux-tube. The flux tuberadius of the baryonic ground state potential is found to be 0.38 \pm 0.03 fm,with vacuum fluctuations suppressed by 7.2 \pm 0.6 %.Comment: 16 pages, final version as accepted for publication in Physical  review D1. Abstract, text, references and some figures have been revise

Gluon flux-tube distribution and linear confinement in baryons