5 research outputs found
Scalar-Vector Bootstrap
We work out all of the details required for implementation of the conformal
bootstrap program applied to the four-point function of two scalars and two
vectors in an abstract conformal field theory in arbitrary dimension. This
includes a review of which tensor structures make appearances, a construction
of the projectors onto the required mixed symmetry representations, and a
computation of the conformal blocks for all possible operators which can be
exchanged. These blocks are presented as differential operators acting upon the
previously known scalar conformal blocks. Finally, we set up the bootstrap
equations which implement crossing symmetry. Special attention is given to the
case of conserved vectors, where several simplifications occur.Comment: 76 pages, v3 moved several details into appendices, expanded
discussion of mixed symmetry projecto
Geodesic Diagrams, Gravitational Interactions & OPE Structures
We give a systematic procedure to evaluate conformal partial waves involving
symmetric tensors for an arbitrary CFT using geodesic Witten diagrams in
AdS. Using this procedure we discuss how to draw a line between the
tensor structures in the CFT and cubic interactions in AdS. We contrast this
map to known results using three-point Witten diagrams: the maps obtained via
volume versus geodesic integrals differ. Despite these differences, we show how
to decompose four-point exchange Witten diagrams in terms of geodesic diagrams,
and we discuss the product expansion of local bulk fields in AdS.Comment: typos corrected, references adde