ar X iv : h ep - l at / 0 20 40 30 v 1 2 9 A pr 2 00 2 Large center vortices and confinement in 3 D Z 2 gauge theory

Large center vortices and confinement in 3D Z 2 gauge theory. Abstract We study the role of large clusters of center vortices in producing confinement in 3D Z2 gauge theory. First, we modify each configuration of a Monte Carlo-generated ensemble in the confined phase by removing the largest cluster of center vortices, and show that the ensemble thus obtained does not confine. Conversely, we show that removing all of the small clusters of center vortices and leaving the largest one only, confinement is preserved, albeit with a string tension significantly smaller than the original one. Remarkably, also the string corrections due to the quantum fluctuations of the confining flux tube are preserved by this transformation. It is widely believed that center vortices play an important role in producing confinement, by disordering the gauge configurations and hence making the Wilson loop decay with the area law. The idea itself is quite old [1, 2], but its investigation by lattice methods was initiated a few years ago in Ref. [3]. A very recent review can be found in [4]. 3D Z 2 gauge theory is the simplest non trivial gauge theory to display confinement: due to the moderate size of its configuration space, it lends itself to very high precision Monte Carlo simulations. Moreover the gauge group coincides with its center, so that the identification of center vortices can be performed without resorting to any gauge-fixing procedure. Therefore Z 2 gauge theory appears as an ideal laboratory to test the actual relevance of center vortices to the mechanism of confinement.