Spectra of the excited giant gravitons from the two loop dilatation operator

Abstract

The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS.