Prove the universal lower bound c_LR ≤ c_eff for conformal interfaces in 2D CFT

Prove that for any two-dimensional conformal field theory with a conformal interface between CFT_L and CFT_R defined by T^(L) − T̄^(L) = T^(R) − T̄^(R), the coefficient c_LR of the stress-tensor cross two-point function across the interface, given by ⟨T^(L)(z1) T^(R)(z2)⟩ = c_LR/[2(z1 − z2)^4], is bounded above by the effective central charge c_eff that governs the entanglement entropy across the interface via S_A = (c_eff/3) ln(L/πϵ); that is, establish c_LR ≤ c_eff for general interface CFTs in 1+1 dimensions.

Background

The paper studies two key quantities characterizing conformal interfaces in 1+1 dimensions: the effective central charge c_eff, which controls entanglement across the interface, and the transmission coefficient encoded by c_LR, which measures energy transmission via the cross-stress-tensor two-point function.

While c_eff and c_LR have been shown to differ in general, the authors present holographic arguments, free field calculations, and defect perturbation theory indicating an inequality c_LR ≤ c_eff. They frame this as a conjecture intended to hold for general CFTs, which would imply that energy transmission across an interface never exceeds information transmission.

The work provides evidence and examples (including saturation cases) but does not give a general CFT proof, leaving the universal validity of c_LR ≤ c_eff as an explicit conjecture.