Abstract:

According to the AdS/CFT correspondence, Witten diagrams in Anti-de Sitter space (AdS) compute 1/N corrections to correlators in a large-N conformal field theory (CFT). Despite recent progress, loop Witten diagrams are far less understood than their flat-space counterparts. We present unitarity methods to study Witten diagrams - one Lorentzian method and one Euclidean. In both approaches, we perform cuts of Witten diagrams that factorize them onto on-shell sub-diagrams. In the Lorentzian method, cuts turn Feynman propagators into on-shell propagators (Wightman functions), as in the standard S-matrix approach. In the Euclidean approach, Witten diagrams are recast as boundary conformal diagrams, and then cuts localize the result onto the expected multi-trace conformal blocks. The Lorentzian and Euclidean methods compute the CFT double-commutator, from which the correlator can be reconstructed. We discuss similar structure in holographic CFTs at finite temperature. Finally, we comment briefly on how these unitarity methods extend tree-level properties of AdS/CFT to loop level for other observables.