### 2.2 Short-distance correlations

On the other hand, if the entropy (3) is non-vanishing, this shows that in the global system
there exist correlations across the surface between modes, which reside on different sides
of the surface. In this review we shall consider the case in which the system in question is a
quantum field. The short-distance correlations that exist in this system have two important
consequences:
- the entanglement entropy becomes dependent on the UV cut-off , which regularizes the
short-distance (or the large-momentum) behavior of the field system
- to leading order in the entanglement entropy is proportional to the area of the surface

For a free massless scalar field the 2-point correlation function in spacetime dimensions has the standard
form

where . Correspondingly, the typical behavior of the entanglement entropy in dimensions
is
where the exact pre-factor depends on the regularization scheme. Although the similarity between (5) and
(6) illustrates well the field-theoretical origin of the entanglement entropy, the exact relation between the
short-distance behavior of 2-point correlation functions in the field theory and the UV divergence of the
entropy is more subtle, as we shall discuss later in the paper.