We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a `boundary central charge' in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that their scaling property agrees with field theory calculations. Finally, we give an example of string theory embedding of this holography by inserting orientifold 8-planes in AdS(4)xCP(3).Comment: 41 pages, 10 figures; v2: further comments on earlier papers about a holographic dual with boundarie

We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N = 6 Chern-Simons theory. We show that D4-branes wrapped on CP 1 or D8branes wrapped on CP 3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U (N ) k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on C 2 /Z n . 1Since there is an energy gap and realistic samples contain impurities, the electrons in the (2+1)dimensional bulk suffer from localization and cannot move around macroscopically, thus the bulk electrons do not contribute to the quantum Hall conductivity. Instead, the electrons can only move along the edges of samples, since the electron orbit at the boundary is stable against impurities. These are called the edge states (for more details, see textbooks [3,1,2,4]). In other words, the quantum Hall fluid is an insulator except at its boundaries. For this reason, quantum Hall states are sometimes called "topological insulator". More general topologically insulating states, including the quantum spin Hall state and its higher-dimensional relatives, have been discussed, fully classified, [6] and experimentally realized recently [7]. In terms of the Chern-Simons theory, the quantization of the Hall conductivity can be understood as follows: since the Chern-Simons action is not gauge invariant in the presence of (1+1)-dimensional boundaries of the (2+1)-dimensional spacetime, there exists a massless chiral scalar field on the boundaries [2] and they contribute to the conductivity. Figure 1: Experimental setup of the quantum Hall effect: a sample of a two-dimensional electron gas is placed on the xy-plane, with a magnetic field B z perpendicular to the plane and an electric field E y along the y-direction. The quantum Hall current flows along the x-direction, perpendicular to the E-field.The main purpose of this paper is to model fractional quantum Hall effect-in particular its Chern-Simons theory description-in string theory and analyze them via AdS/CFT [8]. 8 We will present three different models, each focusing on different aspects of the FQHE. They are summarized as follows.8 Earlier models of embedding the FQHE in string theory mainly used the noncommutative Chern-Simons description (as opposed to holographic description) [9,10,11,12,13,14,15]. Recently a holographic construction of the QHE which is different from ours was realized in [16,17] (for a related setup see [18]). See also [19,20,21] for holographic calculations of the classical Hall effect. 9 This is consistent with the interpretation of fraction...

We use the soft-wall AdS/QCD model to investigate the finite-temperature effects on the spectral function in the vector channel. The dissociation of the vector meson tower onto the AdS black hole leads to the in-medium mass shift and the width broadening in a way similar to the lattice QCD results for the heavy quarkonium at finite temperature. We also show the momentum dependence of the spectral function and find it consistent with screening in a hot wind.

We investigate the finite-temperature spectral functions of heavy quarkonia by using the soft-wall AdS/QCD model. We discuss the scalar, the pseudo-scalar, the vector, and the axial-vector mesons and compare their qualitative features of the melting temperature and growing width. We find that the axial-vector meson melts earlier than the vector meson, while there appears only a slight difference between the scalar and pseudo-scalar mesons which also melt earlier than the vector meson.