| In this dissertation we explore various aspects of the AdS/CFT correspondence, which is a duality between d = 4, N = 4 SYM, and IIB superstring theory on AdS5 x S5 with selfdual RR field strength. String quantization on general backgrounds with fluxes is very difficult. So instead, one uses the duality at the level of canonical fields of supergravity and the corresponding ½-BPS operators in SYM, since they both belong to the shortest multiplets of the superconformal group SU(2, 2|4).; In addition to ½-BPS operators, there are others with non-renormalization properties. One such class of operators is the ¼-BPS operators, which are dual to threshold bound states of elementary supergravity excitations. Their scaling dimension is also determined by their internal quantum numbers. In Chapter 2, we consider scalar composites with the right quantum numbers, and construct ¼-BPS operators as the ones with Og2YM -protected two-point functions. Extended superspace methods (Chapter 3) make it simple to identify and remove descendant pieces from ¼-BPS candidates. In Chapter 4, we compute three-point functions involving ¼-BPS operators, and explain how their non-renormalization translates into statements about the dual supergravity quantities.; But we can go beyond discussing supergravity modes and protected SYM operators. The GS superstring on AdS5 x S5 can be quantized exactly in the limit where the AdS5 radius R → infinity and the R-charge J ∼ R2. String states with finite energy and momentum (BMN states) are then dual to single trace operators with certain phases inserted (BMN operators). BMN operators are another natural generalization of ½-BPS operators, to which they reduce in the zero-momentum limit.; The perturbative expansion of scaling dimensions of BMN operators is in powers of gN/J2. Moreover, one can do perturbation theory around the R → infinity, J ∼ R2 limit. Both expansions have the same regime of validity in string theory and in SYM. In Chapter 5, we calculate the first 1/R2 corrections to BMN states and their energies, and the 1/J corrections for the corresponding BMN operators. We find complete agreement between the dual quantities. |
