  The electromagnetic response of topological insulators and superconductors is
governed by a modified set of Maxwell equations that derive from a topological
Chern-Simons (CS) term in the effective Lagrangian with coupling constant
$\kappa$. Here we consider a topological superconductor or, equivalently, an
Abelian Higgs model in $2+1$ dimensions with a global $O(2N)$ symmetry in the
presence of a CS term, but without a Maxwell term. At large $\kappa$, the gauge
field decouples from the complex scalar field, leading to a quantum critical
behavior in the $O(2N)$ universality class. When the Higgs field is massive,
the universality class is still governed by the $O(2N)$ fixed point. However,
we show that the massless theory belongs to a completely different universality
class, exhibiting an exotic critical behavior beyond the Landau-Ginzburg-Wilson
paradigm. For finite $\kappa$ above a certain critical value $\kappa_c$, a
quantum critical behavior with continuously varying critical exponents arises.
However, as a function $\kappa$ a transition takes place for $|\kappa| <
\kappa_c$ where conformality is lost. Strongly modified scaling relations
ensue. For instance, in the case where $\kappa^2>\kappa_c^2$, leading to the
existence of a conformal fixed point, critical exponents are a function of
$\kappa$.
