Evidence for 3d bosonization from monopole operators

Abstract

We give evidence for 3d bosonization in Conformal Field Theories (CFTs) by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level $k$ and $N$ complex bosons in a large $N,k$ expansion. We first consider the $k=0$ case, where we show that scaling dimensions previously computed to subleading order in $1/N$ can be extrapolated to $N=1$ and matched to $O(2)$ Wilson-Fisher CFT scaling dimensions with around 5\% error, which is evidence for particle-vortex duality. We then generalize the subleading calculation to large $N,k$ and fixed $k/N$, extrapolate to $N=k=1$, and consider monopole operators that are conjectured to be dual to non-degenerate scalar operators in a theory of a single Dirac fermion. We find matches typically with 1\% error or less, which is strong evidence of this so-called `seed' duality that implies a web of 3d bosonization dualities among CFTs.

4 pages plus appendices, no figures. v2 minor typos corrected, submitted for publication

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Cited by in corpus (3)

• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
• Monopoles in Dirac spin liquids and their symmetries from instanton calculus
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter