By Makoto Natsuume

ISBN-10: 4431554408

ISBN-13: 9784431554400

ISBN-10: 4431554416

ISBN-13: 9784431554417

This booklet describes purposes of the AdS/CFT duality to the "real world." The AdS/CFT duality is an concept that originated from string concept and is a strong device for reading strongly-coupled gauge theories utilizing classical gravitational theories. lately, it's been proven that one prediction of AdS/CFT is certainly as regards to the experimental results of the genuine quark–gluon plasma. seeing that then, the AdS/CFT duality has been utilized to varied fields of physics; examples are QCD, nuclear physics, condensed-matter physics, and nonequilibrium physics.

The goal of this publication is to supply history fabrics reminiscent of string thought, black holes, nuclear physics, condensed-matter physics, and nonequilibrium physics in addition to key functions of the AdS/CFT duality in one quantity. The emphasis during the ebook is on a pedagogical and intuitive method targeting the underlying actual strategies. it's also step by step computations for vital effects, that are necessary for beginners.

This booklet could be a precious reference paintings for graduate scholars and researchers in particle physics, basic relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics.

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**Sample text**

48) where 2GM = r+ + r− and GQ2 = r+r− . We chose the dimensions of Q as dimensionless. ) The RN black hole is a solution of the Einstein-Maxwell theory8 : S= d4x √ −g 1 2 1 R− F . 49) The equations of motion from the above action is given by 1 1 Rμν − gμν R = 2G Fμρ Fν ρ − gμν F 2 , 2 4 ∇ν F μν = 0. 51) Here, we check only the Maxwell equation: √ 1 ∇ν F μν = √ ∂ν ( −g F μν ) = 0. 52) When a black hole has an electric charge, Fr 0 = Er = 0, and the only nontrivial √ √ equation is ∂r ( −g F r 0 ) = 0.

Thermodynamics is the theory of many molecules or atoms. According to thermodynamics, one does not have to specify the position and the momentum of each molecule to characterize a thermodynamic system. The system can be characterized only by a few macroscopic variables such as temperature and pressure. The prescription to go from microscopic variables to macroscopic variables is known as the coarse-graining. The black hole is described only by a few parameters. This suggests that somehow the black hole is a coarse-grained description.

52) When a black hole has an electric charge, Fr 0 = Er = 0, and the only nontrivial √ √ equation is ∂r ( −g F r 0 ) = 0. For the above metric, F r 0 = −Fr 0 and −g = r 2 sin2 θ , so the solution to the Maxwell equation is given by Eq. 48). The field strength Fμν is written by the gauge potential Aμ as Fμν = ∂μ Aν − ∂ν Aμ . For our electric field, one may choose the gauge potential A0 as A0 = − Q . 47) has two horizons r = r± , where r± = GM ± 8 G2 M2 − GQ2 . 54) Note the normalization of the Maxwell action.

### AdS/CFT Duality User Guide by Makoto Natsuume

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