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 due to the compactness of the emergent U(1) gauge field. These 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. By obtaining the scaling dimension of monopole operators while constraining their spin quantum number, we explicitly show their organization into multiplets of the QCP flavor symmetry group SU(2)xSU(N). We also discuss 1/N corrections to the scaling dimension of monopoles at a critical point between a DSL and a chiral spin liquid.