What Symmetries are Preserved by a Fermion Boundary State?
Abstract
Usually, a left-moving fermion in d=1+1 dimensions reflects off a boundary to become a right-moving fermion. This means that, while overall fermion parity $(-1)^F$ is conserved, chiral fermion parity for left- and right-movers 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 chiral-parity-preserving 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:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.07369
- arXiv:
- arXiv:2006.07369
- Bibcode:
- 2020arXiv200607369B
- Keywords:
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- High Energy Physics - Theory;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 21 pages