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: AdS3xS3xM4 and AdS5xS5, 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 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 AdS5xS5 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 AdS3xS3xM4 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 AdS3xS3xM4 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.
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