  Topological insulators are characterized by the presence of gapless surface
modes protected by time-reversal symmetry. In three space dimensions the
magnetoelectric response is described in terms of a bulk theta term for the
electromagnetic field. Here we construct theoretical examples of such phases
that cannot be smoothly connected to any band insulator. Such correlated
topological insulators admit the possibility of fractional magnetoelectric
response described by fractional theta/pi. We show that fractional theta/pi is
only possible in a gapped time reversal invariant system of bosons or fermions
if the system also has deconfined fractional excitations and associated
degenerate ground states on topologically non-trivial spaces. We illustrate
this result with a concrete example of a time reversal symmetric topological
insulator of correlated bosons with theta = pi/4. Extensions to electronic
fractional topological insulators are briefly described.
