Topics on AdS/CFT duality and holography

This dissertation presents our study on various aspects of Maldacena's AdS/CFT duality and on a generalization of it from the point of view of holography.; The AdS/CFT duality states that supergravity on anti-de Sitter (AdS) background is equivalent to a local conformal field theory (CFT) on the boundary at infinity of AdS space. One way to generalize the AdS/CFT duality is to turn on more background fields of supergravity such as the r-form fields. The bulk geometry is no longer AdS, and one finds that in the spirit of AdS/CFT duality, it corresponds to a nonconformal field theory with the radial position of the boundary as the energy scale and with the boundary at infinity as the ultraviolet fixed point. Moreover, one can derive the holographic renormalization group (RG) flows of the field theory from its gravity dual. A specific case of interest is the Neveu-Schwarz 2-form potential on the world volume of a D-brane, the resulting open-string low energy effective field theory has been shown to be a Yang-Mills theory with spacetime noncommutativity. Since spacetime noncommutativity is expected to be a natural ingredient of quantum gravity theory, we wonder if one could understand some of its properties from its gravity dual.; In this dissertation we show that an isotropic noncommutative Yang-Mills theory (NCYM) is dual to a dilatonic gravity theory, and we follow a formalism recently developed by de Boer, Verlinde, and Verlinde to construct its holographic RG flow; especially we find that the central charges of the Weyl anomaly of the NCYM run with the energy scale and satisfy a generalization of the C-theorem.; By recognizing the importance of holography as a guiding principle to quantum gravity, we also discuss some of its general properties from the universality and symmetry (general covariance) considerations. We conclude that (1) the holographic principle should apply to the more general cases such as the cosmological horizon of de Sitter space, and (2) in certain situations field theories in different boundary geometry can be equivalent through bulk diffeomorphisms.