D-Branes in Anti-de-Sitter Space

Citation

Lee, Peter Byungho (2003) D-Branes in Anti-de-Sitter Space. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZE9Y-RP78. https://resolver.caltech.edu/CaltechETD:etd-06022003-200011

Abstract

We investigate the role of Dp-branes, which are p+1 dimensional membranes where open strings end, in two different types of anti-de-Sitter backgrounds: AdS₃ x S₃ x M⁴ and AdS₅ x S⁵, where M⁴ is a compact four-dimensional manifold such as the four-torus T4 or the K3 surface.

In the spirit of the AdS/CFT correspondence, D-brane physics on an anti-de-Sitter space should be captured by a dual conformal field theory defined on the boundary of AdS. Recently, Karch and Randall and DeWolfe, Freedman and Ooguri proposed in that the presence of a single D5-brane in AdS₅ x S⁵ is dual to a defect conformal field theory in which the usual N=4 bulk SYM theory is coupled to a 2+1 dimensional conformal defect field theory. Extending their result, we take the Penrose limit of a single D5-brane embedded in AdS₅ x S⁵ and propose a correspondence between open string states ending on the D5-brane and gauge-invariant operators living on the dual defect conformal field theory. Furthermore, we check this proposal by verifying that the anomalous dimension of the gauge theory operators matches the light-cone Hamiltonian of open strings ending on the D5-brane.

Maldacena has proposed that type IIB string theory compactified on AdS₃ x S₃ x M⁴ is dual to a 1+1 conformal field theory defined on the conformal boundary of AdS₃. In this thesis, we restrict our attention to the study of a D-brane embedded in AdS₃ x S₃ x M⁴ backgrounds and leave the explicit construction of the AdS/CFT correspondence of this setup for future work by others. First, we investigate the spectrum of open strings on AdS₂ branes in AdS₃ in an NS-NS background using the SL(2,R) WZW model. Then, we construct boundary states for the AdS₂ branes in the Euclideanized AdS₃ background and compute the one-loop free energy of open strings stretched between the branes.

Thesis Files