Gaudin models and multipoint conformal blocks: general theory

Self Cite

It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduced fourth order differential operators that measure the choice of 3-point tensor structures for all vertices of 3- and 4-dimensional comb channel conformal blocks. These vertices come associated with a single cross ratio. Remarkably, we identify the vertex operators as Hamiltonians of a crystallographic elliptic Calogero-Moser-Sutherland model that was discovered originally by Etingof, Felder, Ma and Veselov. Our construction is based on a further development of the embedding space formalism for mixed-symmetry tensor fields. The results thereby also apply to comb channel vertices of 5- and 6-point functions in arbitrary dimension.

Section: Review and Summary Of Resultsmentioning

confidence: 99%

Section: Jhep11(2021)182mentioning

confidence: 99%

Section: Group Theoretic Reformulation Of the Vertex Systemmentioning

confidence: 99%

Section: Jhep11(2021)182 1 Introductionmentioning

confidence: 99%

Section: Jhep11(2021)182 1 Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D

Burić¹,

Lacroix

Mann³

et al. 2021

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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.

Shadow celestial amplitudes

Chang

Cui

et al. 2023

We study scattering amplitudes in the shadow conformal primary basis, which satisfies the same defining properties as the original conformal primary basis and has many advantages over it. The shadow celestial amplitudes exhibit locality manifestly on the celestial sphere, and behave like correlation functions in conformal field theory under the operator product expansion (OPE) limit. We study the OPE limits for three-point shadow celestial amplitude, and general 2 → n − 2 shadow celestial amplitudes from a certain class of Feynman diagrams. In particular, we compute the conformal block expansion of the s-channel four-point shadow celestial amplitude of massless scalars at tree-level, and show that the expansion coefficients factorize as products of OPE coefficients.