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We investigate the shear viscosity $eta$ and the entropy density $s$ of strongly coupled $mathcal{N}=4$ super Yang-Mills (SYM) plasma in late time of hydrodynamic evolution with AdS/CFT duality and Bjorken scaling. We use correlation function method proposed by Kovtun, Son and Starinets. We obtain the metric $g_{mu u}$ in a proper time dependent $AdS_{5}$ space through holographic renormalization, whose boundary condition is given by energy-momentum tensor of the plasma in 2+1 dimension with transverse expansion or radial flow. With the metric we compute $eta$ and $s$ of fluids in 1+1 and 2+1 dimension without and with radial flow. We find the ratio $eta/s=1/(4pi)$ in 1+1 dimension consistent with the Kovtun-Son-Starinets bound if next-to-leading terms in proper time are included in the equation of motion for metric perturbations. For 2+1 dimension the result is unchanged in the leading order of transverse rapidity.
This is the draft/updated version of a textbook on real-world applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials suc
We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) sy
We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the membrane paradigm fluid of classical black hole mecha
We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are wrapped around the compact manifold S^{4/7} and are dynamically equivalent to bosonic strings in AdS_5. We thus conveniently identify them as Stringy Membranes. For the case of
We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and