  It is well known that theorems of Lieb-Schultz-Mattis type prohibit the
existence of a trivial symmetric gapped ground state in certain systems
possessing a combination of internal and lattice symmetries. In the continuum
description of such systems the Lieb-Schultz-Mattis theorem is manifested in
the form of a quantum anomaly afflicting the symmetry. We demonstrate this
phenomenon in the context of the deconfined critical point between a Neel state
and a valence bond solid in an $S =1/2$ square lattice antiferromagnet, and
compare it to the case of $S=1/2$ honeycomb lattice where no anomaly is
present. We also point out that new anomalies, unrelated to the microscopic
Lieb-Schultz-Mattis theorem, can emerge prohibiting the existence of a trivial
gapped state in the immediate vicinity of critical points or phases. For
instance, no translationally invariant weak perturbation of the $S = 1/2$
gapless spin chain can open up a trivial gap even if the spin-rotation symmetry
is explicitly broken. The same result holds for the $S =1/2$ deconfined
critical point on a square lattice.
