  We evaluate the relative entropy on a ball region near the UV fixed point of
a holographic conformal field theory deformed by a fermionic operator of
nonzero vacuum expectation value. The positivity of the relative entropy
considered here is implied by the expected monotonicity of decrease of quantum
entanglement under RG flow. The calculations are done in the perturbative
framework of Einstein-Cartan gravity in four-dimensional asymptotic anti-de
Sitter space with a postulated standard bilinear coupling between axial fermion
current and torsion. By requiring positivity of relative entropy, our result
yields a constraint on axial current-torsion coupling, fermion mass and
equation of state.
