Gravity/Gauge Duality In Higher Derivative Gravities

Gravity/gauge duality,also known as AdS/CFT correspondence,builds up a holo-graphic dictionary connecting gravity theories in d+1 dimensional anti-de Sitter(AdS)spacetime with d-dimensional conformal field theories(CFT)living in the AdS boundary.This holographic dictionary allows us to investigate a variety of aspects in strongly-coupled CFT by studying classical gravities,for example,the conformal anomaly,a-theorem and correlation functions.This thesis aims to introduce a part of author's work related to gravity-gauge duality during the Master Program:gravity/gauge duality for higher deriva-tive gravities at AdS scale.After briefly reviewing the holographic dictionary and the rele-vant techniques,we consider cubic gravities and analyze the equation of motion,Gibbons-Hawking boundary terms and holographic counterterms.In general,the linearized spectrum around AdS vacua of higher derivative gravities contains massless graviton and additional massive modes.We remove all massive modes and focus on massless cubic gravities where the linearized spectrum around AdS vacua only contains massless graviton such that the corresponding CFT is more likely to be unitary.Take cubic Ricci gravity as example,we adopt Fefferman-Graham(FG)expansion to obtain the holographic conformal anomalies in D=5,d=4 with extracting relevant central charges a-charge and c-charge in an abstract way.We also present a simple trick called reduced FG expansion to extract a-charge and c-charge for cubic gravity in D=5,d=4.In addition,we generalize a-charge to gen-eral dimensions and establish a holographic a-theorem provided with additional constrain-s on coupling constants.Moreover,we calculate the covariant holographic stress-tensor two-point functions where the overall coefficients CT charge is a natural generalization of c-charge in arbitrary dimensions.We find that CT charge is related to a-charge by a dif-ferential formula(d-1)CT=l(?)a/(?)l where l is the effective AdS radius,for which the differential formula is verified to be universally applicable for Gauss-Bonnet gravity and more general Lovelock gravity.Subsequently,we explore the holographic energy flux op-erator which is related to stress-tensor three-point function.We present the holographic energy flux parameters t2 and t4 that could determine stress-tensor three-point function in D=5,d=4.