Conformal multi-Regge theory

Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for 2 → 2 scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as matrix elements of the rotation group with definite covariance properties under a subgroup. This allows to use a variety of techniques from harmonic analysis in order to construct a novel algebra of weight-shifting operators. All spinning partial waves are generated by the action of these operators on a set of known scalar seeds. The text is accompanied by a Mathematica notebook to automatically generate partial waves. These results pave the way to a systematic studies of spinning S-matrix bootstrap and positivity bounds.

Section: Discussionmentioning

confidence: 99%

Spinning partial waves for scattering amplitudes in d dimensions

Burić,

Russo,

Vichi

2023

“…Over the past few years, some preliminary steps were made in the attempt to bootstrap higher-point correlation functions, both numerically [14] and analytically [15][16][17][18][19][20]. An immediate obstruction to bootstrapping higher-point correlators is the lack of ready availability JHEP05(2024)299 of higher-point conformal blocks.…”

Section: Introductionmentioning

confidence: 99%

Improving the five-point bootstrap

Poland,

Prilepina,

Tadić

2024

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in $$ {\textrm{AdS}}_3^{\otimes m} $$

Fortin,

Ma,

Parikh

et al. 2024

We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS3 or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-particle wavefunctions on an AdS3 constructed directly in cross-ratio space. This construction generalizes to blocks for a special class of diagrams, which are determined as free-particle wavefunctions in tensor products of AdS3. Conformal blocks for all the remaining topologies are obtained as limits of the free wavefunctions mentioned above. Our results show directly that the integrable models associated with all one- and two-dimensional conformal blocks can be seen as limits of free theory, and manifest a relation between AdS and CFT kinematics that lies outside of the standard AdS/CFT dictionary. We complete the discussion by providing explicit Feynman-like rules that can be used to work out blocks for all topologies, as well as a Mathematica notebook that allows simple computation of Casimir equations and series expansions for blocks, by requiring just an OPE diagram as input.