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Comments on holographic entanglement entropy and RG flows. (English) Zbl 1348.81337

Summary: 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.

MSC:

81T17 Renormalization group methods applied to problems in quantum field theory
81V17 Gravitational interaction in quantum theory
83C99 General relativity
83E30 String and superstring theories in gravitational theory
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