Abstract
We study the role of large clusters of center vortices in producing confinement in $3\mathrm{D}$ ${Z}_{2}$ 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 by 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.
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