QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions

Abstract

Quantum field theory on two- and three-dimensional fuzzy anti-de Sitter spaces is introduced and studied. We find a complete set of solutions to the fuzzy Klein-Gordon equation and identify the commutative limit in which they reduce to classical scalar field modes. After introducing the noncommutative boundary via semi-classical states, the fuzzy modes are used to obtain the boundary two-point function. In both two and three dimensions, this gives an interesting two-parameter deformation of the conformal two-point function. For the fuzzy AdS${}_2$, the two-point function is given explicitly in terms of the Appell function $F_1$.

32 pages, four figures; v2: further elaboration on internal space, interpretation of results, and appendix E added; matches the version published in JHEP

References in corpus (19)

• Building an AdS/CFT superconductor
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• The S-matrix Bootstrap I: QFT in AdS
• Scaling Limits of the Fuzzy Sphere at one Loop
• TASI lectures on AdS/CFT
• A Practical Mini-Course on Applied Holography
• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• Gravity and the Structure of Noncommutative Algebras
• 2D fuzzy Anti-de Sitter space from matrix models
• The fuzzy 4-hyperboloid $H_n^4$ and higher-spin in Yang-Mills matrix models
• Fuzzy de Sitter Space
• Regular Poisson structures on massive non-rotating BTZ black holes
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• Note on correlation functions in conformal quantum mechanics
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields
• Star products on extended massive non-rotating BTZ black holes
• Laplacian on fuzzy de Sitter space
• The fuzzy BTZ