  Algebraic spin liquids, which are exotic gapless spin states preserving all
microscopic symmetries, have been widely studied due to potential realizations
in frustrated quantum magnets and the cuprates. At low energies, such putative
phases are described by quantum electrodynamics in 2+1 dimensions. While
significant progress has been made in understanding this nontrivial interacting
field theory and the associated spin physics, one important issue which has
proved elusive is the quantum numbers carried by so-called monopole operators.
Here we address this issue in the ``staggered-flux'' spin liquid which may be
relevant to the pseudogap regime in high-T_c. Employing general analytical
arguments supported by simple numerics, we argue that proximate phases encoded
in the monopole operators include the familiar Neel and valence bond solid
orders, as well as other symmetry-breaking orders closely related to those
previously explored in the monopole-free sector of the theory. Surprisingly, we
also find that one monopole operator carries trivial quantum numbers, and
briefly discuss its possible implications.
