Related papers: Witten Diagrams Revisited: The AdS Geometry of Con…
We study a homogeneous system of $d+8$ linear partial differential equations (PDEs) in $d$ variables arising from two-dimensional Conformal Field Theories (CFTs) with a $W_3$-symmetry algebra. In the CFT context, $d$ PDEs are third-order…
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…
Quasi-median graphs are a tool commonly used by evolutionary biologists to visualise the evolution of molecular sequences. As with any graph, a quasi-median graph can contain cut vertices, that is, vertices whose removal disconnect the…
The AdS/CFT correspondence is an explicit realization of the holographic principle relating a theory of gravity in a volume of space to a lower dimensional quantum field theory on its boundary. By exploiting elements of quantum error…
We construct smeared CFT operators which represent a scalar field in AdS interacting with gravity. The guiding principle is micro-causality: scalar fields should commute with themselves at spacelike separation. To O(1/N) we show that a…
The differential representation of AdS correlators offers a framework to express exchange Witten diagrams as functions of non-local differential operators applied to contact Witten diagrams. In this paper, we develop the differential…
Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in…
We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal…
We study a class of two-point functions in a conformal field theory near a wedge. This is a set-up with two boundaries intersecting at an angle $\theta$. We compute it as a solution to the Dyson-Schwinger equation of motion for a quartic…
We study the exchange diagrams in the computation of four-point functions of all chiral primary operators in D=4, $\mathcal{N}=4$ Super-Yang-Mills using AdS/CFT correspondence. We identify all supergravity fields that can be exchanged and…
Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in…
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…
The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that…
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 study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base scheme according to the block structures of the fibers. This…
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…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Motivated by AdS/CFT, we address the following outstanding question in large $N$ conformal field theory: given the appearance of a single-trace operator in the ${\cal O}\times{\cal O}$ OPE of a scalar primary ${\cal O}$, what is its total…
In this thesis, we consider two approaches to the study of correlation functions in one-dimensional defect Conformal Field Theories (dCFT$_1$), in particular those defined by 1/2-BPS Wilson line defects in the three- and four-dimensional…
We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary…