Related papers: Simplicity in AdS Perturbative Dynamics
We propose a definition of Mellin amplitudes for conformal correlators involving arbitrary spinning operators in tensor representations of the Lorentz group. These representations cover all bosonic local operators. Our strategy is to…
In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in…
We present a simple general relation between tree-level exchanges in AdS and dS. This relation allows to directly import techniques and results for AdS Witten diagrams, both in position and momentum space, to boundary correlation functions…
We compute the Mellin amplitude of the planar four-point correlator of weight-two half-BPS operators in $\mathcal{N}=4$ SYM at one and two-loop orders in the small 't Hooft coupling expansion. The two-loop Mellin amplitude has an infinite…
We investigate the embedding formalism in conjunction with the Mellin transform to determine tree-level gluon amplitudes in AdS/CFT. Detailed computations of three to five-point correlators are conducted, ultimately distilling what were…
In this paper, we propose a $p$-adic analog of Mellin amplitudes for scalar operators, and present the computation of the general contact amplitude as well as arbitrary-point tree-level amplitudes for bulk diagrams involving up to three…
We propose studying a new representation of on-shell Anti de Sitter (AdS) amplitude in Mellin Momentum space, where it encodes all the dynamical information in Cosmological Correlators. At tree level, we demonstrate that this amplitude has…
We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS amplitudes in terms of conformal generators acting on contact Witten diagrams, which allows us…
We prove that all tree-level $n$-point supergluon (scalar) amplitudes in AdS$_5$ can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar…
We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar $\phi^4$-theory in Euclidean AdS$_4$, by recasting the Witten diagrams as flat space Feynman…
We investigate loop corrections to the four-point function of identical scalar operators in a four-dimensional large $N$ conformal field theory, holographically dual to AdS with a quartic interaction. We focus on the universal part of the…
We consider holographic CFTs and study their large $N$ expansion. We use Polyakov-Mellin bootstrap to extract the CFT data of all operators, including scalars, till $O(1/N^4)$. We add a contact term in Mellin space, which corresponds to an…
This work is an extension of our previous work, hep-th/0204160, which showed how to systematically calculate the high energy evolution of gauge couplings in compact AdS_5 backgrounds. We first directly compute the one-loop effects of…
Alday & Maldacena conjectured an equivalence between string amplitudes in AdS$_5 \times S^5$ and null polygonal Wilson loops in planar $\mathcal{N}=4$ super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with areas of…
We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The resummation…
We study the analytic structure of loop Witten diagrams in Euclidean AdS represented by their conformal partial wave expansions. We show that, as in flat space, amplitude's singularities are associated with non-trivial cuts of the diagram…
In this paper we consider Witten diagrams at one loop in AdS space for scalar $\phi^3+\phi^4$ theory. After using Schwinger parametrization to trivialize the space-time loop integration, we extract the Mellin-Barnes representation for the…
We develop a systematic approach to evaluating AdS loop amplitudes based on the spectral (or "split") representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree…
We provide dramatic evidence that `Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into `left' and `right'…
We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at…