  We study the properties of a class of two-dimensional interacting critical
states -- dubbed algebraic spin liquids -- that can arise in two-dimensional
quantum magnets. A particular example that we focus on is the staggered flux
spin liquid, which plays a key role in some theories of underdoped cuprate
superconductors. We show that the low-energy theory of such states has much
higher symmetry than the underlying microscopic spin system. This symmetry has
remarkable consequences, leading in particular to the unification of a number
of seemingly unrelated competing orders. The correlations of these orders --
including, in the staggered flux state, the Neel vector and the order parameter
for the columnar and box valence-bond solid states -- all exhibit the SAME slow
power-law decay. Implications for experiments in the pseudogap regime of the
cuprates and for numerical calculations on model systems are discussed.
