  Conformal boundary conditions in two-dimensional conformal field theories
manifest lots of mathematical beauty and complexity and in many aspects present
uncharted territory. Even less is known about the relevant boundary
deformations which connect them. A natural approach to the problem is via
conformal perturbation theory, which however becomes quickly intractable and
possibly ambiguous. Relying on the internal consistency of open string field
theory, which has been proved to be a consistent theory of conformal boundary
conditions, we show how to construct nearby fixed points of the two-dimensional
renormalization group flow triggered by weakly relevant operators. As a simple
illustration we calculate the boundary degeneracy $g$ to next-to-leading order
for a generic theory.
