Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact 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 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 $N=2,4$.

18 pages, 6 figures, minor changes

References in corpus (7)

• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Monopoles in CP(N-1) model via the state-operator correspondence
• Large $N_f$ quantum field theory
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Non-perturbative beta function in three-dimensional electrodynamics
• Phase of the fermion determinant in QED_3 using a gauge invariant lattice regularization
• Critical number of fermions in three-dimensional QED

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