The anti-de Sitter(p)/CFT(p-1) correspondence for cases p = 3 and 5
Harlan Robins · CERN Document Server (European Organization for Nuclear Research) · 2001
The AdSp/CFT p −1 correspondence conjectures that a string theory on p-dimensional anti-deSitter space × a smooth (10-p)-dimensional manifold is dual to a superconformal field theory in (p-1) dimensions. In this thesis, after a short review of the correspondence, we examine three applications in detail. The case p = 3 provides an interesting test of the conjecture because CFT 2 has an infinite conformal symmetry which is not the obvious symmetry group of AdS3. However, Brown and Henneaux showed that classical gravity on AdS 3 does have an infinite symmetry group which forms a Virasoro algebra. In the framework of the AdS/CFT correspondence, the Virasoro generators were constructed in string theory on AdS 3 by Giveon, Kutasov, and Seiberg (GKS). We create a formalism for string theory in AdS3 which realizes the Brown-Henneaux Virasoro symmetry and leads to the GKS Virasoro generators. With a semi-classical analysis, many features of the duality are explored. Using our formalism and the correspondence, we derive the Virasoro Ward identities of the boundary CFT. Our work clarifies several aspects of the GKS construction: why the Brown-Henneaux Virasoro algebra can be realized on the first-quantized Hilbert space, to what extent the free-field approximation is valid, and why the Virasoro generators act on the string worldsheet localized near the boundary of AdS3. However, in our construction the Virasoro central charge only arises in second quantized string theory. Following the in depth study of the particular example p = 3, we focus on a potential use of the AdS/CFT correspondence; calcutating glueball masses in QCD. These masses have already been computed in three dimensional non-supersymmetric Yang-Mills theory using the correspondence and found to be in agreement with lattice gauge theory results. The computation was done in the strong coupling limit while the lattice results are valid for weak coupling (continuum limit). In the continuum limit, we expect the supergravity Kaluza-Klein states to decouple because they do not have a counterpart on the Yang-Mills side. However, in the supergravity limit g2YMN → ∞, we find that the masses of the Kaluza-Klein states are comparable to those of the glueballs. We see no signs of decoupling. Finally, we explore the holographic nature of the correspondence. The AdS/CFT correspondence identifies the coordinates of the boundary of anti-de Sitter space with the coordinates of the conformal field theory. We generalize this identification to theories formulated in superspace. As an application of our results, we study a class of Wilson loops in N = 4 super-Yang-Mills theory. A gauge theory computation shows that the expectation values of these loops are invariant under a local κ-symmetry, except at intersections. We identify this with the κ-invariance of the associated string worldsheets in the corresponding bulk superspace.