A bispinor formalism for spinning Witten diagrams

We develop a new embedding-space formalism for AdS(4) and CFT3 that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS(4) and conformal Killing spinors for the boundary CFT3. The more conventional embedding space coordinates XI for the bulk and PI for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin l >= 1, we determine its conservation properties at the unitarity bound. In our CFT3 formalism, we identify an so(5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS(4), can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an R-4 contact interaction in AdS(4). Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.

Automated summary

This study develops a new embedding-space formalism for evaluating Witten diagrams for operators with spin. By determining the conservation properties of boundary operators and using a set of differential operators, Witten diagrams with spinning external legs can be related to Witten diagrams with scalar external legs.