  Recently it is found that, due to Weyl anomaly, a background scalar field
induces a non-trivial Fermi condensation for theories with Yukawa couplings.
For simplicity, the paper consider only scalar type Yukawa coupling and, in the
BCFT case, only for a specific boundary condition. In these cases, the Weyl
anomaly takes on a simple special form. In this paper, we generalize the
results to more general situations. First, we obtain general expressions of
Weyl anomaly due to a background scalar and pseudo scalar field in general 4d
BCFTs. Then, we derive the general form of Fermi condensation from the Weyl
anomaly. It is remarkable that, in general, Fermi condensation is non-zero even
if there was not a non-vanishing scalar field background. Finally, we verify
our results with free BCFT with Yukawa coupling to scalar and pseudo-scalar
background potential with general chiral bag boundary condition and with
holographic BCFT. In particular, we obtain the shape and curvature dependence
of the Fermi condensate from the holographic one point function.
