See also this paper: arxiv-1307.7480: Lattice Non-Perturbative Definition of 1+1D Anomaly-Free Chiral Fermions and Bosons. This paper follows Prof. Wen's general thinking and provide a proof between the following two conditions:

**"Topological Boundary (Gapping) Conditions"**

is equivalent to

**"t' Hooft anomaly matching conditions"**

The proof is given for the case of the a theory with a U(1) symmetry and in 1+1D.

Using this equivalent relation, one can design the **very constrained specific** boundary gapping terms to open the mass gap of the mirror sectors.

The untouched sector in principle can provide a lattice chiral fermion model. (or, for the next step, chiral gauge theory in 1+1D.)

This post imported from StackExchange Physics at 2014-04-05 03:00 (UCT), posted by SE-user Idear