相关论文: Towards Feynman rules for conformal blocks
We give a holographic description of global conformal blocks in two dimensional conformal field theory on the sphere and on the torus. We show that the conformal blocks for one-point functions on the torus can be written as Witten diagrams…
The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this…
Feynman diagrams are calculated by means of their Taylor series expansion in terms of external momenta squared. It is demonstrated in various examples that by the application of conformal mapping and Pad\'{e} approximants, it is possible to…
General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the…
We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes…
We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
We compute tree-level $n$-point scattering amplitudes in scalar field theories in terms of geometric invariants on a fibre bundle. All 0- and 2-derivative interactions are incorporated into a metric on this bundle. The on-shell amplitudes…
The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram)…
We continue studying of global conformal blocks on the torus in a special (necklace) channel. Functions of such multi-point blocks are explicitly found under special conditions on the blocks' conformal dimensions. We have verified that…
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…
Feynman diagrams (notably the triangle diagram) involving heavy enough particles contain branch cuts on the physical sheet - anomalous thresholds - which, unlike normal thresholds and bound-state poles, do not correspond to any asymptotic…
We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…
The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…
We develop the relation between gravitational Wilson line networks, defined as a particular product of Wilson line operators averaged over the cap states, and conformal correlators in the context of the AdS$_2$/CFT$_1$ correspondence. The…
Conformal 3-point correlators of conserved currents play important roles in numerous directions. These correlators are fixed by conformal symmetry up to a few parameters, which are known only at leading order in perturbative expansions. The…
We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…