Related papers: Spinning Mellin Bootstrap: Conformal Partial Waves…
In this note we consider the problem of extracting the corrections to CFT data induced by the exchange of a primary operator and its descendents in the crossed channel. We show how those corrections which are analytic in spin can be…
We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the…
Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are defined as eigenfunctions of the differential Casimir operators for the…
We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials,…
We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of $CFT_d$ four point functions and expands them in terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange functions.…
We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of \cite{Caron-Huot:2017vep}, both from the position space representation as well as…
We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS$_{d+1}$. Employing this…
We generalize Regge theory to correlation functions in conformal field theories. This is done by exploring the analogy between Mellin amplitudes in AdS/CFT and S-matrix elements. In the process, we develop the conformal partial wave…
By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…
We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the…
In this note, we derive a Mellin space version of the Lorentzian inversion formula for CFTs by explicitly integrating over the cross-ratios in $d=2$ and $d=4$ spacetime dimensions. We use the simplicity of the Mellin representation of…
We generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in \cite{arXiv:1806.10919, arXiv:1808.00612} to arbitrary space-time dimensions. By using the inversion…
We propose a definition of Mellin amplitudes for conformal correlators involving arbitrary spinning operators in tensor representations of the Lorentz group. These representations cover all bosonic local operators. Our strategy is to…
We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed…
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an…
We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us…
We further develop celestial Mellin amplitudes arXiv:2412.11992 to capture the exchange of particles with spin. For massless external scalar fields, we derive closed-form celestial Mellin amplitudes for a spin-1 and spin-2…
We employ a hybrid approach in determining the anomalous dimension and OPE coefficient of higher spin operators in the Wilson-Fisher theory. First we do a large spin analysis for CFT data where we use results obtained from the usual and the…
In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function ${\bf{F}}_4$. We also construct…
We explore conformal primary wavefunctions for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient…