  We study 't Hooft anomalies of discrete groups in the framework of
(1+1)-dimensional multiscale entanglement renormalization ansatz states on the
lattice. Using matrix product operators, general topological restrictions on
conformal data are derived. An ansatz class allowing for optimization of MERA
with an anomalous symmetry is introduced. We utilize this class to numerically
study a family of Hamiltonians with a symmetric critical line. Conformal data
is obtained for all irreducible projective representations of each anomalous
symmetry twist, corresponding to definite topological sectors. It is
numerically demonstrated that this line is a protected gapless phase. Finally,
we implement a duality transformation between a pair of critical lines using
our subclass of MERA.
