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Using numerical simulations, a vortex is studied in the broken phase of the$(2+1)$-d $O(2)$-symmetric scalar field theory in the vicinity of theWilson-Fisher fixed point. The vortex is an infraparticle that is surrounded bya cloud of Goldstone bosons. The $L$-dependence of the vortex mass in a finite$C$-periodic volume $L^2$ leads to the determination of the renormalized vortexcharge.

Mass and Charge of the Quantum Vortex in the $(2+1)$-d $O(2)$ Scalar Field Theory