توصيفگر ها :
ميدان اوليه , تانسورانرژي تكانه , جبر و يراسورو , فضاي باد دوسيته , همانند سازي , ژئودزيك , تابع دونقطه اي , ميدان اسكالر , تقارن مجانبي , دوگاني CFT , Ads
چكيده انگليسي :
Conformal Field Theory and BTZ Black Hole Hamid Razaghian razaghian hamid@gmail com May 3 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language Persian loran@cc iut ac irDr Farhang LoranAbstractThe conformal eld theory as a subset of quantum eld theory has the conformal symmetry Intwo dimensions the conformal elds are representation of virasoro algebra that its generators arethe modes of energy momentum tensor of the theory The conformal transformations in two dimen sions are holomorphic maps in a way that its generators produce an algebra with in nite dimension By use of conformal symmetry we can determine the form of two and three point functions Theelements of energy momentum tensor which is traceless are divided into two holomorphic and anti holomorphic parts In the free boson theory the central charge is equal to 1 And the derivatives of elds are elds with conformal dimension of 1 In fermionic theory the central charge is equal to 1 2and has the conformal dimension of 1 2 The solutions of three dimensional BTZ black hole has beenobtained from the Einstein equation in three dimensions with the negative cosmological constant This black hole has two internal and external event horizons which divide the space time into threedi erent regions Killing vectors belong to BTZ metric have time and angular symmetries Antide sitter spaces are also the solutions of Einstein s equation with negative cosmological constant andone can extract BTZ metric by identifying some of its coordinates there are two integral constantsin BTZ black hole metric that are assumed as its mass and angular momentum In the case thatmass and angular momentum are equal extremal case the event horizons are coincided together We solve the geodesic equations by use of killing vectors then we extract the motion s trajectoryof time like light like and space like particles One can see that massless particles can escape fromblack hole s gravitational eld If exists a conformal coupled massless scalar eld in backgroundBTZ space the propagators of this eld can be obtained from the equation of motion Then byidentifying coordinates and image method one can get the two point functions in BTZ coordinates By use of action and two point functions we calculate the expectation value of energy tensor ofstatic and rotating black holes For static and rotating black holes the energy tensor on the eventhorizon has a nite value but in singular point will diverge If we perturb the metric such that the eld s formations remain invariant some symmetries would appear which they are symmetry gener ators that produce the virasoro algebra It is shown that the global charges of a gauge theory mayyield a nontrivial central extension of the asymptotic symmetry algebra The asymptotic symmetrygroup in that case is either R x SO 2 or the pseudo conformal group in two dimensions dependingon the boundary conditions adopted at spatial in nity In the latter situation a nontrivial centralcharge appears in the algebra of the canonical generators which turns out to be just the Virasorocentral charge In the other word in the boundary of anti de sitter space which the tensor metric istwo dimensional a conformal eld can be de ned the central charge is equal to c 3l 2G Keywords Conformal Field Theory CFT Primary Field Tensor Energy Momentum Con formal weight Virasoro Aljebra Radial Quantization Tree Dimensional Black Hole BTZ Anti de Sitter Space ADS Identi cation Geodesic extremal Black Hole Green Function Two Point Function Scalar Filed Assymptotic Symmetry Duality AdS CFT
