State-Dependent Divergences in the Entanglement Entropy

Understand

We show the entanglement entropy in certain quantum field theories to contain state-dependent divergences.

• Both perturbative and holographic examples are exhibited.
• However, quantities such as the relative entropy and the generalized entropy of black holes remain finite, due to cancellation of divergences.
• We classify all possible state-dependent divergences that can appear in both perturbatively renormalizeable and holographic covariant $d\le 6$ quantum field theories.