Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings

Understand

We consider states of bosons in two dimensions that do not support anyons in the bulk, but nevertheless have stable chiral edge modes that are protected even without any symmetry.

• Such states must have edge modes with central charge $c=8k$ for integer $k$.
• While there is a single such state with $c=8$, there are, naively, two such states with $c=16$, corresponding to the two distinct even unimodular lattices in 16 dimensions.
• However, we show that these two phases are the same in the bulk, which is a consequence of the uniqueness of signature $(8k +n, n)$ even unimodular lattices.