# Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED

## TL;DR

This paper uses Monte Carlo simulations to directly measure the scaling dimension of monopole operators in three-dimensional non-compact QED with various fermion flavors, providing insights into the theory's infrared behavior.

## Contribution

It introduces a novel Monte Carlo method to determine monopole scaling dimensions directly in 3D QED, analyzing different flavor numbers and comparing with large-N predictions.

## Key findings

- Scaling dimension for N=12 matches large-N value.
- Deviations for N=2 and 4 are small and positive.
- Higher order corrections are mildly significant for low N.

## 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 non-compact 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 $N=2,4$.