Holographic RG flows from IIB supergravity

The AdS/CFT correspondence has proved to be an important part of the string theory. Its essence is the duality between the ten-dimensional string theory and field theories on "brane worlds" in spaces of lower dimensions. Thus far, the AdS/CFT correspondence remains a very well supported conjecture, but has not been proven in all generality. The original research I did for this dissertation provides one of the first examples that support conjecture in the strongly coupled, non-perturbative limit of the field theory.; In collaboration with N. Warner and K. Pilch I have analyzed the critical points of scalar potential of the five-dimensional compactification of IIB supergravity. The most significant result was the discovery of supersymmetric critical point, corresponding to N = 1 supersymmetric, four-dimensional Yang-Mills field theory on the brane. This fixed point was subsequently shown to be the same as one discovered by Leigh and Strassler by means of pure field theoretical methods.; In this thesis, I have also studied a general class of N = 1 flows in which all three chiral multiplets have independent masses and the corresponding Yang-Mills scalars can develop supersymmetry preserving VEVs. The gaugino also is allowed to develop a VEV. An especially detailed investigation was done for the N = 1 supersymmetric Coulomb Branch flows, where scalar VEVs "swamp" the corresponding masses. The two types of flow I found, differ by the rate at which mass vanish in the infrared limit.; Finally, I have examined the RG flows via 10-dimensional IIB supergravity. This work also included a conjecture and test of "lifting" formulae, which provide a solution to IIB supergravity equations from the five dimensional parameters of the RG flow. I found the metric to be generalization of extremal rotating D3 branes and I mapped five-dimensional parameters to those of rotating branes. This allowed me to retrieve the brane distribution for each type of the flow. I also determined how the direction of tensor fields depends on the brane distribution.