AdS/CFT correspondence and symmetry breaking

We study, using the dual AdS description, the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar field s. In such vacua, operators built out of the scaler fields acquire expectat ion values, and we show how to calculate them from the behavior of perturba tions to the AdS background near the boundary. Specific examples include th e N = 4 SYM theory, and theories on D3-branes placed on orbifolds and conif olds, We also clarify some subtleties of the AdS/CFT correspondence that ar ise in this analysis. In particular, we explain how scalar fields in AdS sp ace of sufficiently negative mass-squared can be associated with CFT operat ors of two possible dimensions. All dimensions are bounded from below by (d -2)/2; this is the unitarity bound for scalar operators in d-dimensional fi eld theory. We further argue that the generating functional for correlators in the theory with one choice of operator dimension is a Legendre transfor m of the generating functional in the theory with the other choice. (C) 199 9 Elsevier Science B.V. All rights reserved.