Characterizing the quantum critical point between a Dirac spin liquid and an antiferromagnet

The spin-1/2 kagome Heisenberg antiferromagnet hosts a putative quantum spin liquid phase for which a candidate ground state is the Dirac spin liquid. At low energies, this state is described by quantum electrodynamics in 2+1 dimensions with 2 N_f = 4 flavors of two-component gapless spinons. We describe a transition to a coplanar antiferromagnetic (AFM) phase by coupling the spinons to a vectorial bosonic order parameter. We find a non-trivial quantum critical point and compute critical exponents using a one-loop d=4-ε expansion. The compactness of the U(1) gauge field allows topological configurations named monopoles which must condense to induce the AFM phase. We classify the monopole operators by their symmetries and comment on their gauge invariance. Using the state-operator correspondence, we compute the scaling dimensions of the monopole operators in the large N_f limit and find non-trivial hierarchy.