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Boundary conditions for Majorana fermions in d=1+1 dimensions fall into oneof two SPT phases, associated to a mod 2 anomaly. Here we consider boundaryconditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. Ingeneral, the left-moving and right-moving fermions carry different chargesunder this symmetry, and implementation of the boundary condition requires newdegrees of freedom, which manifest themselves in a boundary central charge,$g$.  We follow the boundary RG flow induced by turning on relevant boundaryoperators. We identify the infra-red boundary state. In many cases, theboundary state flips SPT class, resulting in an emergent Majorana mode neededto cancel the anomaly. We show that the ratio of UV and IR boundary centralcharges is given by $g^2_{IR} / g^2_{UV} = {\rm dim}\,({\cal O})$, thedimension of the perturbing boundary operator. Any relevant operatornecessarily has ${\rm dim}({\cal O}) < 1$, ensuring that the central chargedecreases in accord with the g-theorem.

Boundary RG Flows for Fermions and the Mod 2 Anomaly