I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement.
As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator.
Time permitting, I will also expand the result to 6D and 4D.
Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture.
The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].