Related papers: Spinning Witten Diagrams
We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT$_d$ using geodesic Witten diagrams in AdS$_{d+1}$. Using this procedure we discuss how to draw a line between the tensor…
We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the…
In this letter we provide a complete holographic reconstruction of the cubic couplings in the minimal bosonic higher-spin theory in AdS$_{d+1}$. For this purpose we also determine the OPE coefficients of all single-trace conserved currents…
We develop the embedding formalism for odd dimensional Dirac spinors in AdS and apply it to the (geodesic) Witten diagrams including fermionic degrees of freedom. We first show that the geodesic Witten diagram (GWD) with fermion exchange is…
We explicitly calculate a Witten diagram with general spinor field exchange on $(d+1)$-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the…
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external…
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we…
We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of…
We develop a new embedding-space formalism for AdS$_4$ and CFT$_3$ 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…
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 show the AdS/CFT correspondence between the conformal partial wave and the geodesic Witten diagram with anti-symmetric exchange. To this end, we introduce the embedding space formalism for anti-symmetric fields in AdS. Then we prove that…
We develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly…
An explicit analytic formula is presented that computes the conformal (super-)block decomposition of any free scalar or half-BPS diagram in 1d, 2d or 4d CFTs, with various supersymmetries, including none. We prove our formula by exploiting…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…
Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, making it extremely difficult to search for…
We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)-conserved representations. In a basis…
We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave…
Witten diagrams provide a perturbative framework for calculations in Anti-de-Sitter space, and play an essential role in a variety of holographic computations. In the case of this study in AdS$_2$, the one-dimensional boundary allows for a…
We derive new integral identities for AdS propagators and further develop the Wilson network expansion for AdS Feynman diagrams. In particular, we demonstrate that four-point contact and exchange scalar diagrams in two dimensions can be…
Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches…