A Kontorovitch-Lebedev-Fourier momentum space is constructed for de Sitter QFT where the dS frequency labels unitary representations, making equations algebraic and propagators simple like in flat space.
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Implications of conformal invariance in momentum space
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abstract
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple-K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. We develop systematic methods for explicitly evaluating the triple-K integrals. In odd dimensions they are given in terms of elementary functions while in even dimensions the results involve dilogarithms. In some cases, the triple-K integrals diverge and subtractions are necessary and we show how such subtractions are related to conformal anomalies. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals and how to evaluate these integrals, while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.
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representative citing papers
Derives integro-differential boundary equations from bulk locality for scale-breaking cosmological correlators with oscillating heavy-field masses and solves them analytically and numerically to reveal enhanced collider signals.
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 double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.
Derives universal quadratic response of 3D CFT free energy to S^3 squashing proportional to c_T and constructs thermal effective action for high-T Seifert manifolds with explicit Wilson coefficients.
Tree-level gluon correlators in AdS4 decompose into energy poles with residues given by flat-space amplitudes, curvature corrections captured by lower-point amplitudes with merged data via AdS Berends-Giele currents.
Different dimensional regularization schemes agree with each other and with unitarity; new analytic eta regulators simplify the work and fix the imaginary part of one-loop coefficients by the logarithmic running of the real part under scale invariance and Bunch-Davies conditions.
Thermal two-point functions of scalar CFT operators at zero spatial separation are reconstructed from their discontinuities via Hurwitz zeta kernels, with OPE coefficients as the only dynamical input.
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.
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
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.
Tree-level Yang-Mills de Sitter wavefunctions through six points are reconstructed from cosmological cuts into cut-detectable gluings plus a current-conservation completion, matching Feynman rules and suggesting an all-n scalar-tubing structure.
Constructs deformed vertex operators in a topological string description of T T-bar deformed tensionless AdS3/CFT2 and computes their exact tree-level two-point functions.
Anomaly-induced dilaton-like corrections in the hard kernel significantly modify pion GFFs at large Q^{2} within a factorization approach using Sudakov resummation and a Gaussian TMD wave function.
The paper derives a correspondence between boundary terms and field redefinitions for cosmological correlators and classifies non-vanishing boundary contributions in massive-exchange diagrams under dS isometries and broken boosts.
Proposal for an experimental test of conformal invariance in critical phenomena via grazing-incidence scattering that checks a momentum-space differential constraint on the cross-section.
The bulk-to-bulk photon propagator in Euclidean AdS is derived in axial, Coulomb and covariant gauges, with the simplest position-space form in the Fried–Yennie gauge ξ=d/(d−2).
Computes O(1/N) corrections to central charges C_J and C_T in conformal QED_d-GNY and scalar QED_d models, obtains scaling dimensions of adjoint bilinears, and finds reasonable agreement with SO(5) DQCP estimates from bootstrap and fuzzy sphere.
In QCD factorization, the pion trace anomaly cancels in A_π(Q²) but is important in D_π and dominates the TJJ contribution to the trace form factor, refining the hierarchy versus lattice data.
Thermal backreaction modifies de Sitter geometry so that late-exiting modes produce a blue-tilted spectrum n_S ~ 2 while the boundary theory matches the 3d Sp(N) model flow.
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
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.
A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.
citing papers explorer
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De Sitter Momentum Space
A Kontorovitch-Lebedev-Fourier momentum space is constructed for de Sitter QFT where the dS frequency labels unitary representations, making equations algebraic and propagators simple like in flat space.
-
Every Wrinkle Carries A Memory: An Integro-differential Bootstrap for Features in Cosmological Correlators
Derives integro-differential boundary equations from bulk locality for scale-breaking cosmological correlators with oscillating heavy-field masses and solves them analytically and numerically to reveal enhanced collider signals.
-
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.
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Cosmological Correlators in KLF and the Double-Exchange
The double-exchange cosmological correlator is computed in KLF space, yielding a double series over hypergeometric functions that improves on prior four-layer representations.
-
CFTs on Squashed Spheres and the Thermal Effective Action
Derives universal quadratic response of 3D CFT free energy to S^3 squashing proportional to c_T and constructs thermal effective action for high-T Seifert manifolds with explicit Wilson coefficients.
-
On the amplitude expansion of gluon correlators in $\textrm{AdS}_4$
Tree-level gluon correlators in AdS4 decompose into energy poles with residues given by flat-space amplitudes, curvature corrections captured by lower-point amplitudes with merged data via AdS Berends-Giele currents.
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Unitary and Analytic Renormalisation of Cosmological Correlators
Different dimensional regularization schemes agree with each other and with unitarity; new analytic eta regulators simplify the work and fix the imaginary part of one-loop coefficients by the logarithmic running of the real part under scale invariance and Bunch-Davies conditions.
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The analytic bootstrap at finite temperature
Thermal two-point functions of scalar CFT operators at zero spatial separation are reconstructed from their discontinuities via Hurwitz zeta kernels, with OPE coefficients as the only dynamical input.
-
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.
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Differential Equations for Massive Correlators
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
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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.
-
From Cosmological Cuts to Yang--Mills Wavefunctions in de Sitter Space
Tree-level Yang-Mills de Sitter wavefunctions through six points are reconstructed from cosmological cuts into cut-detectable gluings plus a current-conservation completion, matching Feynman rules and suggesting an all-n scalar-tubing structure.
-
$\boldsymbol{T\overline{T}}$ correlators from tensionless strings
Constructs deformed vertex operators in a topological string description of T T-bar deformed tensionless AdS3/CFT2 and computes their exact tree-level two-point functions.
-
The Gravitational Form Factor of the Pion in Perturbative QCD with a Dilaton Interaction
Anomaly-induced dilaton-like corrections in the hard kernel significantly modify pion GFFs at large Q^{2} within a factorization approach using Sudakov resummation and a Gaussian TMD wave function.
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On Cosmological Correlators with Boundary Contributions
The paper derives a correspondence between boundary terms and field redefinitions for cosmological correlators and classifies non-vanishing boundary contributions in massive-exchange diagrams under dS isometries and broken boosts.
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Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments
Proposal for an experimental test of conformal invariance in critical phenomena via grazing-incidence scattering that checks a momentum-space differential constraint on the cross-section.
-
Bulk-to-bulk photon propagator in AdS
The bulk-to-bulk photon propagator in Euclidean AdS is derived in axial, Coulomb and covariant gauges, with the simplest position-space form in the Fried–Yennie gauge ξ=d/(d−2).
-
Central charges $C_J$ and $C_T$ in QED$_d$-GNY model and scalar QED$_d$
Computes O(1/N) corrections to central charges C_J and C_T in conformal QED_d-GNY and scalar QED_d models, obtains scaling dimensions of adjoint bilinears, and finds reasonable agreement with SO(5) DQCP estimates from bootstrap and fuzzy sphere.
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The Pion Gravitational Form Factors and the Trace Anomaly in QCD Factorization
In QCD factorization, the pion trace anomaly cancels in A_π(Q²) but is important in D_π and dominates the TJJ contribution to the trace form factor, refining the hierarchy versus lattice data.
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The thermal backreaction of a scalar field in de Sitter spacetime. II. Spectrum enhancement and holography
Thermal backreaction modifies de Sitter geometry so that late-exiting modes produce a blue-tilted spectrum n_S ~ 2 while the boundary theory matches the 3d Sp(N) model flow.
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A Match Made in Heaven: Linking Observables in Inflationary Cosmology
In dynamical Chern-Simons inflation the parity-odd trispectrum is a double copy of the mixed bispectrum and parity-odd power spectrum via a prior factorization formula.
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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.
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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.
-
The Carrollian Kaleidoscope
A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.