We consider perturbation defects obtained by perturbing a 2D conformal field
theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk
theory flows to an infrared fixed point described by another CFT, the defect
flows to a conformal defect between the ultraviolet and infrared fixed point
CFTs. For short bulk renormalization group flows connecting two fixed points
which are close in theory space we find a universal perturbative formula for
the boundary entropy of the corresponding conformal perturbation defect. We
compare the value of the boundary entropy that our formula gives for the flows
between nearby Virasoro minimal models Mm with the boundary entropy of the
defect constructed by Gaiotto in [1] and find a match at the first two orders
in the 1/m expansion.Comment: 24 pages, 2 figure
