this talk, I will construct a symmetry protected topological phase of bosons in
3d with particle number conservation and time reversal symmetries, which is the
direct bosonic analogue of the familiar electron topological insulator. The
construction employs a parton decomposition of bosons, followed by condensation
of parton-monopole composites. The surface of the resulting state supports a
gapped symmetry respecting phase with intrinsic toric code topological order
where both e and m anyons carry charge 1=2.
is well-known that one signature of the 3d electron topological insulator is
if the system is coupled to a compact electromagnetic gauge eld, a monopole in
bulk acquires a half-odd-integer polarization charge. I will discuss the
for the constructed topological insulator of bosons: a monopole can remain
neutral, but its statistics are transmuted from bosonic to fermionic. This
Witten eect" guarantees that the surface is either gapless, symmetry
an intrinsic topological order.