  A conformal field theory (CFT) in dimension $d\geq 3$ coupled to a planar,
two-dimensional, conformal defect is characterized in part by a "central
charge" $b$ that multiplies the Euler density in the defect's Weyl anomaly. For
defect renormalization group flows, under which the bulk remains critical, we
use reflection positivity to show that $b$ must decrease or remain constant
from ultraviolet to infrared. Our result applies also to a CFT in $d=3$ flat
space with a planar boundary.

High Energy Physics - Theory;Mesoscale and Nanoscale Physics;Statistical Mechanics;Strongly Correlated Electrons