# AdS amplitudes Scattering amplitudes in AdS are related to correlators of the CFT. ## Refs - CFT correlator as AdS amplitudes - [[2010#Penedones]] - [[2012#Raju]] - [[2011#Maldacena, Pimentel]]: uses [[0373 Spinor helicity formalism|spinor-helicity]] formalism - all-loop - [[2024#Banados, Bianchi, Munoz, Skenderis]] - Feynman rules - [[2024#Chu, Kharel]] - recursion and factorisation - [[2024#Mei, Mo]] - twistor space correlators - [[2024#Baumann, Mathys, Pimentel, Rost]] - [[0152 Colour-kinematics duality|colour-kinematics duality]] - [[2020#Amstrong, Lipstein, Mei]] ## Relation to [[0091 Boundary causality|boundary causality]] Calculating graviton scattering amplitude at loop levels is equivalent to doing a path integral perturbatively, where the path integral is over the metric, so one can ask whether including metrics that violate boundary causality gives rise to an amplitude that violates boundary causality. See also: [[0115 Superluminality]]. ## Propagator - see [[0103 Two-point functions]] - see [[lec_DHokerFreedman]] ch.6.3. has a few refs ## 1-Loop results - heat kernel expression - $\operatorname{Tr} e^{-\Delta^{(\Lambda)} t}=\sum_{k=0}^{\infty} t^{(k-4) / 2} \int \mathrm{d}^{4} x \sqrt{g}\, b_{k}^{(\Lambda)}$ - $180(4 \pi)^{2} b_{4}^{(\Lambda)}(1,1)=189 R_{\mu \nu \rho \sigma} R^{\mu \nu \rho \sigma}-756 \Lambda^{2}$ $180(4 \pi)^{2} b_{4}^{(\Lambda)}\left(\frac{1}{2}, \frac{1}{2}\right)=-11 R_{\mu \nu \rho \sigma} R^{\mu \nu \rho \sigma}+984 \Lambda^{2}$ $180(4 \pi)^{2} b_{4}^{(\Lambda)}(0,0)=R_{\mu \nu \rho \sigma} R^{\mu \nu \rho \sigma}+636 \Lambda^{2}$ - shown in [[1980#Christensen, Duff]] for general spins, and copied in [[DilkesDuffLiuSati2001]] ## Discontinuity in the massless limit - in flat space, there is a discontinuity between the exact massless case and the massless *limit* - massless case has 2 d.o.f., but massive case has 5 - experiments rule out the massive case in real life - in AdS, the discontinuity disappears at tree-level - [[KoganMouslopoulosPapazoglou2000]] and [[Porrati2000]] - but reappears at 1-loop - [[DilkesDuffLiuSati2001]]