A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
Canonical reference
Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
Canonical reference. 80% of citing Pith papers cite this work as background.
7
Pith papers citing it
Background
80% of classified citations
abstract
We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space 3-point functions in terms of certain integrals involving a product of three Bessel functions (triple-K integrals). The triple-K integrals diverge when the dimensions of operators satisfy certain relations and we discuss how to obtain renormalised 3-point functions in all cases. There are three different types of divergences: ultralocal, semilocal and nonlocal, and a given divergent triple-K integral may have any combination of them. Ultralocal divergences may be removed using local counterterms and this results in new conformal anomalies. Semilocal divergences may be removed by renormalising the sources, and this results in CFT correlators that satisfy Callan-Symanzik equations with beta functions. In the case of non-local divergences, it is the triple-K representation that is singular, not the 3-point function. Here, the CFT correlator is the coefficient of the leading nonlocal singularity, which satisfies all the expected conformal Ward identities. Such correlators exhibit enhanced symmetry: they are also invariant under dual conformal transformations where the momenta play the role of coordinates. When both anomalies and beta functions are present the correlators exhibit novel analytic structure containing products of logarithms of momenta. We illustrate our discussion with numerous examples, including free field realisations and AdS/CFT computations.
citation-role summary
background 5
citation-polarity summary
fields
hep-th 7verdicts
UNVERDICTED 7roles
background 5representative citing papers
A new symplectic bi-Grassmannian representation encodes CFT4 Wightman correlators via integrals over mutually symplectically orthogonal n-planes aligned with kinematics, reproducing known 2- and 3-point structures compactly and revealing double-copy properties.
In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
A new Super-Grassmannian integral formalism for N=1 SCFT3 correlators enforces symmetries manifestly and relates all component functions to one, enabling construction of AdS4 gluon correlators from gluino ones.
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
A new Super-Grassmannian organizes SCFT3 correlators with manifest symmetries and connects AdS4 results to N=4 SYM amplitudes in the flat-space limit.
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.
citing papers explorer
-
Kontorovich-Lebedev-Fourier Space for de Sitter Correlators
A Kontorovich-Lebedev-Fourier space is built for (d+1)-dimensional de Sitter correlators from the Casimir operator of SO(1,d+1), producing rational propagators and Feynman rules that turn tree and loop diagrams into spectral integrals and orthogonality relations.
-
The Conformal Grassmannian: A Symplectic Bi-Grassmannian for $CFT_ 4$ Correlators
A new symplectic bi-Grassmannian representation encodes CFT4 Wightman correlators via integrals over mutually symplectically orthogonal n-planes aligned with kinematics, reproducing known 2- and 3-point structures compactly and revealing double-copy properties.
-
When AdS$_3$ Grows Hair: Boson Stars, Black Holes, and Double-Trace Deformations
In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
-
The $\mathcal{N}=1$ Super-Grassmannian for CFT$_3$ and a Foray on AdS and Cosmological Correlators
A new Super-Grassmannian integral formalism for N=1 SCFT3 correlators enforces symmetries manifestly and relates all component functions to one, enabling construction of AdS4 gluon correlators from gluino ones.
-
A Compact Story of Positivity in de Sitter
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
-
Super-Grassmannians for $\mathcal{N}=2$ to $4$ SCFT$_3$: From AdS$_4$ Correlators to $\mathcal{N}=4$ SYM scattering Amplitudes
A new Super-Grassmannian organizes SCFT3 correlators with manifest symmetries and connects AdS4 results to N=4 SYM amplitudes in the flat-space limit.
-
An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.