Quantum ${\varphi }^4$ Theory in AdS${}_4$ and its CFT Dual

We compute the two- and four-point holographic correlation functions up to the second order in the coupling constant for a scalar ${\varphi }^4$ theory in four-dimensional Euclidean anti-de Sitter space. Analytic expressions for the anomalous dimensions of the leading twist operators are found at one loop, both for Neumann and Dirichlet boundary conditions.