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.