4-point function from conformally coupled scalar in AdS${}_6$

Abstract

We explore conformally coupled scalar theory in AdS${}_6$ extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling $\lambda$. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension $\Delta =3$, from the classical solutions. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the $\Delta =3$ scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect $SO(5)$ rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic $n$-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of $n$-point function by connecting $l$-point functions each other where $l<n$. In the co-linear limit, these $n$-point functions reproduce the conformal $n$-point functions of $\Delta =3$ scalar operators in $d=5$ Euclidean space addressed in arXiv:2001.05379.

29 pages, 9 figures, 2 subsections are added, one of the subsections are omitted and a few references are added

References in corpus (7)

• Conformal $n$-point functions in momentum space
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
• An étude of momentum space scalar amplitudes in AdS
• New relation for AdS amplitudes
• On Some Hypergeometric Solutions of the Conformal Ward Identities of Scalar 4-point Functions in Momentum Space
• Stochastic quantization and holographic Wilsonian renormalization group
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Cited by in corpus (4)

• On spinning loop amplitudes in Anti-de Sitter space
• Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS${}_4$
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation
• First order formalism of holographic Wilsonian renormalization group: Langevin equation