Return to Question

Consider two subsystems $A$ and $B$.

In a local quantum field theory defined on the composite system $AB$, why is the divergent piece of the entanglement entropy of subsystem $A$ given by a local integral over the entangling surface $\partial A$?

For reference, see equation (19.3) on page 176 of these notes.

Consider two subsystems $A$ and $B$.

In a local quantum field theory defined on the composite system $AB$, why is the divergent piece of the entanglement entropy of subsystem $A$ given by a local integral over the entangling surface $\partial A$?

For reference, see equation (19.3) on page 176 of Thomas Hartman's notes on Quantum Gravity and Black Holes.

Consider two subsystems $A$ and $B$.

In a local quantum field theory defined on the composite system $AB$, why is the divergent piece of the entanglement entropy of subsystem $A$ given by a local integral over the entangling surface $\partial A$?

For reference, see equation (19.3) on page 176 of these notes.

How does this follow from the fact that, when we renormalize a local quantum field theory, we are only allowed to add local counterterms to the Lagrangian?

Why do non-local terms come from the infrared physics of a quantum field theory?

Consider two subsystems $A$ and $B$.

In a local quantum field theory defined on the composite system $AB$, why is the divergent piece of the entanglement entropy of subsystem $A$ given by a local integral over the entangling surface $\partial A$?

For reference, see equation (19.3) on page 176 of these notes.