AdS Gravity As A SO(2,d)Gauge Theory

The study of holographic duality is the forefront of recent studies in theoretical physics.As the most successful example of the holographic duality,the AdS/CFT correspondence implies a duality between the quantum gravity in D= d+1 dimensional anti-de Sitter space and the d-dimensional conformal field theory.In recent years,a general principle was noticed in the studies of the AdS/CFT.That is,the global symmetry in the boundary field theory is dual to the gauge symmetry in the bulk theory.This principle have played very important roles in the applications of AdS/CFT.Since the global symmetry of the boundary CFT in AdS space is described by SO(2,d)conformal group,the general principle implies that we can reformulate the d+1 dimensional AdS gravity theory as a SO(2,d)gauge theory.Besides D = 3 and 4,such kind of reformulation was not established in a general dimension until our works.In this thesis we will review the construction of the SO(2,d)gauge theory of AdS gravity theory comprehensively.In this thesis,we first introduce the basic knowledge about conformal field theory and AdS/CFT correspondence.In particular,various forms of AdS gravity theory are disscussed in detail.Based on these preparations,we find a way of uplifting the fundamental degree of freedom of the gravity,in which the SO(2,d)local gauge symmetry appears manifestly.Then,for general dimensions,the AdS gravity theory is reformulated as a SO(2,d)gauge theory.In this formalism,the pull back of the bulk equation of motion onto a co-dimension one hypersurface(50)can be naturally related to the SO(2,d)conservation law under a local energy scale of the dual CFT.Providing the non-anomalous condition of these conservation laws is valid for any local energy scale,the bulk Einstein equation will be automatically implied.In this paper,the AdS gravity theory is reformulated as a SO(2,d)gauge theory,and then the dual relationship between the motion equation of bulk gravity and the non-anomalous condition of boundary SO(2,d)conservation law is established.From this,the holographic structure of bulk gravity dynamics is obtained by means of pure CFT.