Related papers: The beginning of the endpoint bootstrap for confor…
This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $\delta$, is used to…
We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of…
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to sum rules that suppress the double-twist sector of…
We analyze the bootstrap approach (a dual optimization method to the variational approach) to one-dimensional spin chains, leveraging semidefinite programming to extract numerical results. We study how correlation functions in the ground…
In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the…
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…
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…
The constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions. The prescriptions can be applied to both unitary and non unitary theories allowing for the study of the spectrum of…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring…
We discuss an idea of how 3D critical exponents can be determined by Conformal Field Theory techniques.
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…
Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained…
We initiate a study of the bootstrap programme for field theories with BMS symmetry. Specifically, we look at two-dimensional field theories with BMS3 symmetry and, using highest weight representations, we construct the BMS bootstrap…
We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents…
The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite…
Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such…
We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect.…