Renormalization of Entanglement Entropy and the Gravitational Effective Action

Understand

The entanglement entropy associated with a spatial boundary in quantum field theory is UV divergent, with the leading term proportional to the area of the boundary.

• For a class of quantum states defined by a path integral, the Callan-Wilczek formula gives a geometrical definition of the entanglement entropy.
• We show that, for this class of quantum states, the entanglement entropy is rendered UV-finite by precisely the counterterms required to cancel the UV divergences in the gravitational effective action.
• In particular, the leading contribution to the entanglement entropy is given by the renormalized Bekenstein-Hawking formula, in accordance with a proposal of Susskind and Uglum.