SciPost Phys. 10, 010 (2021) ·
published 19 January 2021
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Boundary conditions for Majorana fermions in d=1+1 dimensions fall into one
of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary
conditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. In
general, the left-moving and right-moving fermions carry different charges
under this symmetry, and implementation of the boundary condition requires new
degrees of freedom, which manifest themselves in a boundary central charge,
$g$.
We follow the boundary RG flow induced by turning on relevant boundary
operators. We identify the infra-red boundary state. In many cases, the
boundary state flips SPT class, resulting in an emergent Majorana mode needed
to cancel the anomaly. We show that the ratio of UV and IR boundary central
charges is given by $g^2_{IR} / g^2_{UV} = {\rm dim}\,({\cal O})$, the
dimension of the perturbing boundary operator. Any relevant operator
necessarily has ${\rm dim}({\cal O}) < 1$, ensuring that the central charge
decreases in accord with the g-theorem.
