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

arXiv comment21 pages

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Cited by in corpus (6)

• Comments on Symmetric Mass Generation in 2d and 4d
• Fermionization of conformal boundary states
• Monopole-fermion scattering and varying Fock space
• Quantum Information Theory of the Gravitational Anomaly
• Monopoles Entangle Fermions
• Boundary condition and reflection anomaly in $2+1$ dimensions