Related papers: Spinning Conformal Correlators
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
We introduce simple group-theoretic techniques for classifying conformally-invariant tensor-structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and $n\geq 4$-point functions of…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
We present a classification of conformally-invariant three-point tensor structures in $d$ dimensions that parallels the classification of three-particle scattering amplitudes in $d+1$ dimensions. Using a set of canonically-normalized…
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…
We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ in a coordinate and index free formalism using a $d+2$ dimensional ambient space. We expand the embedding space formalism to cover spinor…
Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study…
We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with…
Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators…
Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…
We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder…
We report some recent progress in the computation of the n-point correlation functions of conserved currents in a class of four dimensional conformal field theories with higher spin symmetry. Global conformal invariance leads to very strong…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts…
We review the relation between the "embedding" formalism and spinorial projective space. The latter is more convenient when treating spin (and indispensable for supersymmetry), as it maintains manifest conformal symmetry while using…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…