Non-Unitary Conformal Interfaces in Unitary CFTs

We design a class of non-unitary conformal interfaces within unitary CFTs, analyzed from both field-theoretic and lattice perspectives. Because these interfaces are non-unitary, neither probability nor energy is conserved, and in particular leading to amplification. In addition to investigating energy transmission, we study entanglement across such interfaces by computing the entanglement entropy. When the entanglement cut is placed precisely at the interface, the entanglement entropy exhibits logarithmic scaling with system size. As in the unitary case, an effective central charge can be extracted from this scaling and used to characterize the interfaces. Remarkably, we find that the effective central charge exceeds the bulk central charge and can, in fact, become unbounded. We also construct the exact boundary state for these interfaces via the folding trick, thereby establishing a complete boundary CFT framework for these non-unitary conformal interfaces.