Monopole hierarchy at a quantum critical point between a Dirac spin liquid and an antiferromagnet

Certain frustrated 2D quantum magnets may be described at low energy by a Dirac spin liquid (DSL) which is a version of quantum electrodynamics with 2N flavors of two-component gapless Dirac spinons. A DSL also hosts monopole excitations that drive the confinement of the spinons. We revisit the hierarchy among monopole operators with different quantum numbers at the quantum critical point (QCP) between a DSL and an antiferromagnet. We describe the organization of monopoles in multiplets of the QCP flavor symmetry group SU(2) x SU(N). The scaling dimension in each magnetic spin sector is obtained at leading order in N using the state-operator correspondence. We also discuss 1/N corrections to the scaling dimension of monopoles at a critical point between a DSL and a chiral spin liquid.