توصيفگر ها :
ميدان اوليه , تابع همبستگي , تانسور تكانه انرژي , جيرويراسورد , كوانتش شعاعي , سياه چاله ي BT Z , ژئودزي , سيا ه چاله ايستا , گرانش اينشتين
چكيده انگليسي :
Conformal Symmetry and Anti de Sitter Space in 2 1 Dimensions Masoud Hassanpour Hasanpour masoud@gmail com May 22 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Dr Farhang Loran loran@cc iut ac irAbstractThe holographic principle is a way to solve the problem of gravitational quantization According to thishypothesis we can describe any event that happens inside a volume by using a theorem that has been written onthe surface In this thesis we explain the duality between a conformal field theory in two dimensional spacesand anti de Sitter 2 1 dimensional space This explanation is a good evidence for this hypothesis At first we investigate the conformal field theory in 2 dimension by representing its formalization and itsimportant subjects The procedure is based on some constraints that we put on correlation functions accordingto symmetries We do this work by introduction of energy momentum tensor central charge the modeexpansion and the Hilbert space of our theory The elements of energy momentum tensor which is traceless aredivided into two holomorphic and antiholomorphic parts we obtain these quantities for free fermionic and freebosonic theory In the free boson theory the central charge is equal to 1 And the derivative of field are fieldswith conformal dimension of 1 In fermionic theory the central charge is equal to 1 2 and has the conformaldimension of 1 2 After that we focus on the free theorem on torus by using Hamiltonian interpretation Thesymmetries on the torus would cause some constraints on partition function of the theory As an example weapply the fermionic theory to that After CFT2 survey we should elucidate anti de Sitter space in 2 1 dimension In this part we clarify thesolution for BTZ black hole and its metric characters This metric is the solution of Einstein field equations withnegative cosmological constant and has two internal and external event horizons which divide the space timeinto three different regions Killing vectors belong to BTZ metric it have time and angular symmetries In BTZmetric there is a singularity in causal structure and we will show this by geodesic analysis of stable black hole we introduce space like time like and light like geodesics that penetrate into the r2 0 region In continuum we solve this problem by regularization of metric Then we pay attention to conformal coupled scalar fieldquantization in BTZ background By image method we obtain Green function for rotational and stable blackholes In extremal case we find out Green function by limitation process from the Green function of rotationalblack hole Then we calculate the quantum energy momentum tensor for those states For static rotating andextreme black holes the energy tensor on the event horizon has a finite value but in singular point will diverge At last we consider duality of AdS3 CFT2 This has been done by introduction of asymptotic symmetry forAdS3 and this fact that the algebra between the generators of this symmetry is isomorphic to asymptoticsymmetry generators of CFT2 So that the symmetry generators produce the virasoro algebra and the centralcharge for it is equal to c 3l 2G The conformal weight of dual operator for a massive scalar field conformalcoupled scalar field and two point function bulk to boundary have been represented Keywords Conformal Field Theory CFT Primary Field Conformal Weight Energy Momentum Tensor Virasoro Algebra Central Charge Radial Quantization BTZ Black Hole Anti de Sitter Space ADS Identification Geodesic Extremal Black Hole Green Function Two Point Function Scalar Field HolographicPrinciple Asymptotic Symmetry Duality AdS CFT Einstein Gravity Duality Gravity CFT
