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.

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