2011/02/23 by Suvrat Raju · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.83.126002
published as Phys.Rev.D83:126002,2011 · 45 pages
arxiv created 2011/02/23 · openalex publication_date 2011/06/03 · arxiv updated 2011/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We expand on the results of our recent letter [Phys. Rev. Lett. 106, 091601 (2011)], where we presented new recursion relations for correlation functions of the stress-tensor and conserved currents in conformal field theories with an AdSd+1 dual for d\ensuremath≥4. These recursion relations are derived by generalizing the Britto-Cachazo-Feng-Witten (BCFW) relations to amplitudes in anti-de Sitter space (AdS) that are dual to boundary correlators, and are usually computed perturbatively by Witten diagrams. Our results relate vacuum-correlation functions to integrated products of lower-point transition amplitudes, which correspond to correlators calculated between states dual to certain normalizable modes. We show that the set of ``polarization vectors'' for which amplitudes behave well under the BCFW extension is smaller than in flat-space. We describe how transition amplitudes for more general external polarizations can be constructed by combining answers obtained by different pairs of BCFW shifts. We then generalize these recursion relations to supersymmetric theories. In AdS, unlike flat-space, even maximal supersymmetry is insufficient to permit the computation of all correlators of operators in the same multiplet as a stress-tensor or conserved current. Finally, we work out some simple examples to verify our results.