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Joint HEP-TH Seminar
One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS$_3^{\otimes m}$
One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS$_3^{\otimes m}$
Organizers
Hongfei Shu
, Rui-Dong Zhu
, Hao Zou
Speaker
Wenjie Ma
Time
Wednesday, December 6, 2023 3:00 PM - 4:00 PM
Venue
A3-4-312
Online
Zoom 559 700 6085
(BIMSA)
Abstract
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 AdS$_3$ or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-particle wavefunctions on an AdS$_3$ 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 AdS$_3$. 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.