The paper explores the AdS/CFT correspondence, focusing on the vacuum states of field theories where gauge symmetries are broken by scalar field expectation values. The authors analyze specific examples, including the $\mathcal{N}=4$ SYM theory and theories on D3 branes placed on orbifolds and conifolds. They clarify subtleties in the AdS/CFT correspondence, such as the association of scalar fields in AdS space with CFT operators of two possible dimensions, and the Legendre transform relationship between these dimensions. The paper also discusses the mass spectrum and operator dimensions, providing a detailed derivation of correlation functions and one-point functions in the presence of sources. Additionally, it examines symmetry breaking in more complex scenarios, such as threebranes on the conifold, and the global structure of supergravity solutions. The authors conclude by discussing the limitations and possibilities of symmetry breaking in these contexts.The paper explores the AdS/CFT correspondence, focusing on the vacuum states of field theories where gauge symmetries are broken by scalar field expectation values. The authors analyze specific examples, including the $\mathcal{N}=4$ SYM theory and theories on D3 branes placed on orbifolds and conifolds. They clarify subtleties in the AdS/CFT correspondence, such as the association of scalar fields in AdS space with CFT operators of two possible dimensions, and the Legendre transform relationship between these dimensions. The paper also discusses the mass spectrum and operator dimensions, providing a detailed derivation of correlation functions and one-point functions in the presence of sources. Additionally, it examines symmetry breaking in more complex scenarios, such as threebranes on the conifold, and the global structure of supergravity solutions. The authors conclude by discussing the limitations and possibilities of symmetry breaking in these contexts.