Related papers: Cut-touching linear functionals in the conformal b…
We propose a bootstrap program for CFTs near intersecting boundaries which form a co-dimension 2 edge. We describe the kinematical setup and show that bulk 1-pt functions and bulk-edge 2-pt functions depend on a non-trivial cross-ratio and…
The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…
We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to, the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory, and deduce the related…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Conformal defects spontaneously break part of the symmetry algebra of a bulk CFT. We show that the broken Ward identities imply very general sum rules on the defect CFT data as well as on the DOE data of bulk operators, which we call defect…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We review 2d CFT in the bootstrap approach, and sketch the known exactly solvable CFTs with no extended chiral symmetry: Liouville theory, (generalized) minimal models, limits thereof, and loop CFTs, including the $O(n)$, Potts and $PSU(n)$…
We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap…
This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…
Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the…
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information…
We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the…
We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave…
We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization…