c-theorem of the entanglement entropy

We holographically investigate the renormalization group flow in a two-dimensional conformal field theory deformed by a relevant operator. If the relevant operator allows another fixed point, the UV conformal field theory smoothly flows to a new IR conformal field theory. From the holographic point of view, such a renormalization group flow can be realized as a dual geometry interpolating two different AdS boundaries. On this interpolating geometry, we investigate how the c-function of the entanglement entropy behaves along the RG flow analyt- ically and numerically, which reproduces the expected central charges of UV and IR. We also show that the c-function monotonically decreases from UV to IR without any phase transition.Comment: 24 pages, 8 figure

Instability of Charged Anti-de Sitter Black Holes

We study the instability of charged anti-de Sitter black holes in four or higher-dimension under fragmentation. The instability of fragmentation breaks the black hole into two black holes. We have found that the region near extremal or massive black holes become unstable under fragmentation. These regions depend not only on the mass and charge of initial black hole but also those of the fragmented one. The instability in higher-dimension is qualitatively similar to that of four-dimension. The detailed instabilities are numerically investigated.Comment: 12 pages, 5 figure