Numerical determination of monopole scaling dimension in parity-invariant three-dimensional noncompact QED

Abstract

We present a direct Monte Carlo determination of the scaling dimension of a topological defect operator in the infrared fixed point of a three-dimensional interacting quantum field theory. For this, we compute the free energy to introduce the background gauge field of the $Q=1$ monopole-antimonopole pair in three-dimensional noncompact QED with $N=2$, 4 and 12 flavors of massless two-component fermions, and study its asymptotic logarithmic dependence on the monopole-antimonopole separation. We estimate the scaling dimension in the $N=12$ case to be consistent with the large-$N$ (free fermion) value. We find the deviations from this large-$N$ value for $N=2$ and 4 are positive but small, implying that the higher-order corrections in the large-$N$ expansion become mildly important for $N=2$, 4.