  We describe a $p$-dimensional conformal defect of a free Dirac fermion on a
$d$-dimensional flat space as boundary conditions on a conformally equivalent
space $\mathbb{H}^{p+1} \times \mathbb{S}^{d-p-1}$. We classify allowed
boundary conditions and find that the Dirichlet type of boundary conditions
always exists while the Neumann type of boundary condition exists only for a
two-codimensional defect. For the two-codimensional defect, a double trace
deformation triggers a renormalization group flow from the Neumann boundary
condition to the Dirichlet boundary condition, and the free energy at UV fixed
point is always larger than that at IR fixed point. This provides us with
further support of a conjectured $C$-theorem in DCFT.

High Energy Physics - Theory