Related papers: Gaudin Models and Multipoint Conformal Blocks III:…
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…
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and…
In the present work, we study celestial correlators of light transformed gluon operators at tree level. We also discuss the transformation of light transformed operators under the action of 4D translations. The two, three and four-point…
Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra's radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension…
We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some…
We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible…
We search for a logarithmic 3-form representing the 6-point MHV gravity amplitude, requiring poles only on physical channels and residues matching factorization. Working in the Orlik-Solomon algebra on a De Concini-Procesi wonderful model,…
A method for obstructing symmetry enhancement in numerical conformal bootstrap calculations is proposed. Symmetry enhancement refers to situations where bootstrap studies initialised with a certain symmetry end up allowing theories with…
We study the two-point function of local operators in the presence of a defect in a generic conformal field theory. We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel…
We study five-point correlators of the $\sigma$, $\epsilon$, and $\epsilon'$ operators in the critical 3d Ising model. We consider the $\sigma \times \sigma$ and $\sigma \times \epsilon$ operator product expansions (OPEs) and truncate them…
We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>, where Phi…
We define and compute the four-dimensional thermal $n$-point conformal block in the projection channel using oscillator representations on $\mathbb{S}^1_\beta \times \mathbb{S}^3$. This is done by evaluating a class of integrals over the…
In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the pillow geometry and thereby crossing symmetry gets translated into a modular property. We use these modular features to derive a universal asymptotic formula for OPE…
Current studies of WN Toda field theory focus on correlation functions such that the WN highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W3 Toda 4-point functions with multiplicity in the…
Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…
We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…
We derive higher moments in the statistical distribution of OPE coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure 3D gravity. The n-th cyclic non-Gaussian contraction of…
We study the conformal bootstrap for a 4-point function of fermions $\langle\psi\psi\psi\psi\rangle$ in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions.…
We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry…
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in…