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

Abstract

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.

38 pages, many diagrams, replaced with the revised version

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• CFT in AdS and boundary RG flows
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• On spinning loop amplitudes in Anti-de Sitter space
• From bulk loops to boundary large-N expansion
• Opacity from Loops in AdS
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• Loops in AdS: From the Spectral Representation to Position Space II
• Polyakov-Mellin Bootstrap for AdS loops
• On one loop corrections in higher spin gravity
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Bulk renormalization and the AdS/CFT correspondence
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• Energy level splitting for weakly interacting bosons in a harmonic trap
• Boundary correlators in WZW model on AdS${}_2$
• Loops in dS/CFT
• Exploring Confinement in Anti-de Sitter Space
• Holographic S-fold theories at one loop
• Bootstrapping Witten diagrams via differential representation in Mellin space
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• Time-periodicities in holographic CFTs
• Simplicity of AdS Supergravity at One Loop
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• Recursive construction of the operator product expansion in curved space
• Constructing CFTs from AdS flows
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• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS