Emanant symmetries and anomalies for (2+1)d Dirac spin liquid

We study global symmetries of Dirac spin liquids (DSL) in (2+1)d lattice spin systems. The DSL state is constructed by fermionic partons, whose low-energy theory is described by Dirac fermions interacting with emergent U(1) gauge field, i.e. QED₃. By analyzing how the lattice symmetries embed into the emergent symmetries of the continuum theory, we determine the 't Hooft anomalies of the emanant symmetry and how they manifest in finite-size systems through lattice quantum numbers. We compare the field-theoretic results with parton wavefunctions for DSLs.