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

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 the Wilson-Fisher fixed point. The vortex is an infraparticle that is surrounded by a 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 vortex charge.