Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields

Abstract

We continue the study of the nocommutative $Ad{S}_2/CF{T}_1$ correspondence. We extend our previous results obtained for a free massless scalar field to the case of a massive scalar field. Both the free and interacting cases are considered. For both cases it is confirmed that to the leading order in noncommutative corrections the 2- and 3-point correlation functions have the form that is assumed by some (yet unspecified) dual $CFT$. We also argue that there does not exist a map which connects the commutative model to its non-commutative counterpart, and therefore the conformal behaviour of the noncommutative correlators is a non-trivial result.

34 pages

References in corpus (4)

• The fuzzy 4-hyperboloid $H_n^4$ and higher-spin in Yang-Mills matrix models
• Matrix Model Cosmology in Two Space-time Dimensions
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Conformal quantum mechanics and holography in noncommutative space-time

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• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• Noncommutative $Ad{S}_2$ I: Exact solutions
• Noncommutative $Ad{S}_2$ II: The Correspondence Principle
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions