Topological insulator of bosons in 3d via dyon condensation and the statistical Witten effect.



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PIRSA Number: 
13040117

Abstract

In
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.

It
is well-known that one signature of the 3d electron topological insulator is
the Witten

eect:
if the system is coupled to a compact electromagnetic gauge eld, a monopole in

the
bulk acquires a half-odd-integer polarization charge. I will discuss the
corresponding

phenomenon
for the constructed topological insulator of bosons: a monopole can remain

electrically
neutral, but its statistics are transmuted from bosonic to fermionic. This
\sta-

tistical
Witten eect" guarantees that the surface is either gapless, symmetry
broken or

carries
an intrinsic topological order.