The a-theorem and entanglement entropy

Abstract

The a-theorem is demonstrated for the RG flows of entanglement entropy in two and four dimensions. In four dimensions we relate it to the term quadratic in intrinsic derivative of the dilaton along the entangling surface in the dilaton entropy. The a-theorem, similarly to the c-theorem in two dimensions, then follows from the positivity of the 2-point function of stress-energy tensor. We suggest that the a-theorem, provided it is properly reformulated in terms of the entanglement entropy, may follow from the c-theorem.