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We study boundary states for Dirac fermions in d=1+1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (-1)^F, which are characterised by the existence of an unpaired Majorana zero mode.
In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped
Two-dimensional SU$(N)$ gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of gluinoball bound states whose spectrum has been studied using nume
A global symmetry of a quantum field theory is said to have an t Hooft anomaly if it cannot be promoted to a local symmetry of a gauged theory. In this paper, we show that the anomaly is also an obstruction to defining symmetric boundary conditions.
Continuum models for time-reversal (TR) invariant topological insulators (TIs) in $d geq 3$ dimensions are provided by harmonic oscillators coupled to certain $SO(d)$ gauge fields. These models are equivalent to the presence of spin-orbit (SO) intera
We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or d