1202.2068 (Robert C. Myers et al.)

Comments on Holographic Entanglement Entropy and RG Flows    [PDF]

Robert C. Myers, Ajay Singh

Using holographic entanglement entropy for strip geometry, we construct a
candidate for a c-function in arbitrary dimensions. For holographic theories
dual to Einstein gravity, this c-function is shown to decrease monotonically
along RG flows. A sufficient condition required for this monotonic flow is that
the stress tensor of the matter fields driving the holographic RG flow must
satisfy the null energy condition over the holographic surface used to
calculate the entanglement entropy. In the case where the bulk theory is
described by Gauss-Bonnet gravity, the latter condition alone is not sufficient
to establish the monotonic flow of the c-function. We also observe that for
certain holographic RG flows, the entanglement entropy undergoes a 'phase
transition' as the size of the system grows and as a result, evolution of the
c-function may exhibit a discontinuous drop.

View original: http://arxiv.org/abs/1202.2068