The area operator and fixed area states in conformal field theories

Understand

The fixed area states are constructed by gravitational path integrals in previous studies.In this paper we show the dual of the fixed area states in conformal field theories (CFTs).These CFT states are constructed by using spectrum decomposition of reduced density matrix $\rho_A$ for a subsystem $A$.

• For 2 dimensional CFTs we directly construct the bulk metric, which is consistent with the expected geometry of the fixed area states.
• For arbitrary pure geometric state $|\psi\rangle$ in any dimension we also find the consistency by using the gravity dual of R\'enyi entropy.
• We also give the relation of parameters for the bulk and boundary state.