14 research outputs found
The Superconformal Xing Equation
Crossing symmetry provides a powerful tool to access the non-perturbative
dynamics of conformal and superconformal field theories. Here we develop the
mathematical formalism that allows to construct the crossing equations for
arbitrary four-point functions in theories with superconformal symmetry of type
I, including all superconformal field theories in dimensions. Our advance
relies on a supergroup theoretic construction of tensor structures that
generalizes an approach which was put forward in \cite{Buric:2019dfk} for
bosonic theories. When combined with our recent construction of the relevant
superblocks, we are able to derive the crossing symmetry constraint in
particular for four-point functions of arbitrary long multiplets in all
4-dimensional superconformal field theories.Comment: 49 page
The fuzzy BTZ
Abstract We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black hole carries a covariant differential calculus, satisfies Einstein’s equations and has a constant negative curvature. The construction passes through a larger space, the fuzzy anti-de Sitter, and implements discrete BTZ identifications as conjugations by a unitary operator. We derive the spectrum of the suitably regularised radial coordinate: it consists of a continuum of scattering states outside the horizon r + and an infinite discrete set of bound states inside
Defect Conformal Blocks from Appell Functions
We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell’s function F