What Symmetries are Preserved by a Fermion Boundary State?
Abstract
Usually, a leftmoving fermion in d=1+1 dimensions reflects off a boundary to become a rightmoving fermion. This means that, while overall fermion parity $(1)^F$ is conserved, chiral fermion parity for left and rightmovers individually is not. Remarkably, there are boundary conditions that do preserve chiral fermion parity, but only when the number of Majorana fermions is a multiple of 8. In this paper we classify all such boundary states for $2N$ Majorana fermions when a $U(1)^N$ symmetry is also preserved. The fact that chiralparitypreserving boundary conditions only exist when $2N$ is divisible by 8 translates to an interesting property of charge lattices. We also classify the enhanced continuous symmetry preserved by such boundary states. The state with the maximum such symmetry is the $SO(8)$ boundary state, first constructed by Maldacena and Ludwig to describe the scattering of fermions off a monopole
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.07369
 Bibcode:
 2020arXiv200607369B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 21 pages