The paper explores the AdS/CFT correspondence in the context of field theories with broken gauge symmetry, using the dual AdS description to study vacua where scalar fields acquire expectation values. It discusses specific examples, including N=4 SYM, D3-branes on orbifolds and conifolds, and clarifies subtleties in the AdS/CFT correspondence. The key result is that scalar fields in AdS space with sufficiently negative mass-squared can correspond to CFT operators of two possible dimensions. The unitarity bound for scalar operators in d dimensions is $ (d-2)/2 $, and the generating functional for correlators in one choice of operator dimension is a Legendre transform of the generating functional in the other choice. The paper also analyzes the mass spectrum and operator dimensions, showing that for certain masses, two different quantum field theories can arise from the same Lagrangian. It discusses the implications for correlation functions and the role of boundary conditions in the AdS/CFT correspondence. The paper concludes with an analysis of symmetry breaking in the context of threebranes on the conifold, showing how different configurations can lead to different vacua in the dual field theory.The paper explores the AdS/CFT correspondence in the context of field theories with broken gauge symmetry, using the dual AdS description to study vacua where scalar fields acquire expectation values. It discusses specific examples, including N=4 SYM, D3-branes on orbifolds and conifolds, and clarifies subtleties in the AdS/CFT correspondence. The key result is that scalar fields in AdS space with sufficiently negative mass-squared can correspond to CFT operators of two possible dimensions. The unitarity bound for scalar operators in d dimensions is $ (d-2)/2 $, and the generating functional for correlators in one choice of operator dimension is a Legendre transform of the generating functional in the other choice. The paper also analyzes the mass spectrum and operator dimensions, showing that for certain masses, two different quantum field theories can arise from the same Lagrangian. It discusses the implications for correlation functions and the role of boundary conditions in the AdS/CFT correspondence. The paper concludes with an analysis of symmetry breaking in the context of threebranes on the conifold, showing how different configurations can lead to different vacua in the dual field theory.