We have studied a holographically dual description of superconductor in (2 + 1)-dimensions in the presence of applied magnetic field, and observed that there exists a critical value of magnetic field, below which a charged condensate can form via a second order phase transition.

The holographic model for S-wave high T c superconductors developed by Hartnoll, Herzog, and Horowitz is generalized to describe D-wave superconductors. The 3 þ 1 dimensional gravitational theory consists of a symmetric, traceless second-rank tensor field and a Uð1Þ gauge field in the background of the anti-de Sitter black hole. Below T c the tensor field, which carries the Uð1Þ charge, undergoes the Higgs mechanism and breaks the Uð1Þ symmetry of the boundary theory spontaneously. The phase transition characterized by the D-wave condensate is second order with the mean field critical exponent ¼ 1=2.As expected, the AC conductivity is isotropic below T c , and the system becomes superconducting in the DC limit but has no hard gap.

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We investigate drag force in a thermal plasma of N=4 super Yang-Mills theory via both fundamental and Dirichlet strings under the influence of non-zero NSNS B-field background. In the description of AdS/CFT correspondence the endpoint of these strings correspondes to an external monopole or quark moving with a constant electromagnetic field. We demonstrate how the configuration of string tail as well as the drag force obtains corrections in this background. 1

We have modified the holographic model of Saremi and Son [12] by using a charged black brane, instead of a neutral one, such that when the bulk pseudo scalar (θ) potential is made of θ 2 and θ 4 terms, parity can still be broken spontaneously in the boundary theory. In our model, the 3+1 dimensional bulk has a pseudo scalar coupled to the gravitational Chern-Simons term in the anti de Sitter charged black brane back ground. Parity could be broken spontaneously in the bulk by the pseudo scalar hairy solution and give rise to non-zero Hall viscosity at the boundary theory.

We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy.Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture. *

We study the fermionic spectral function in a holographic superconductor model. At zero temperature, the black hole has zero horizon and hence the entropy of the system is zero after the back reaction of the condensate is taken into account. We find the system exhibits the famous peak-dip-hump lineshape with a sharp low-energy peak followed by a dip then a hump at higher energies. This feature is widely observed in the spectrum of several high-Tc superconductors. We also find a linear relation between the gap in the fermionic spectrum and the condensate, indicating the condensate is formed by fermion pairing.

We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov-Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein-Hawking area