General Two-point Functions Research Articles

Holographic description for correlation functions

We study general correlation functions of various quantum field theories in the holographic setup. Following the holographic proposal, we investigate correlation functions via a geodesic length connecting boundary operators. We show that this holographic description can reproduce the known two- and three-point functions of conformal field theory. Using this holographic method, we further study general two-point functions of a two-dimensional thermal conformal field theory (CFT) and of a scalar field theory living in a de Sitter or anti–de Sitter space. Due to the nontrivial thermal or curvature effect, the two-point functions in an IR limit show different scaling behaviors from those of the UV CFT. We study such nontrivial IR scaling behaviors by applying the holographic method. Published by the American Physical Society 2024

TWO-POINT FUNCTIONS IN AFFINE SL(N) CURRENT ALGEBRA

In this letter the explicit form of general two-point functions in affine SL (N) current algebra is provided for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately read off.

TWO-POINT FUNCTIONS AND QUANTUM FIELDS IN DE SITTER UNIVERSE

We present a theory of general two-point functions and of generalized free fields in d-dimensional de Sitter space-time which closely parallels the corresponding Minkowskian theory. The usual spectral condition is now replaced by a certain geodesic spectral condition, equivalent to a precise thermal characterization of the corresponding “vacuum” states. Our method is based on the geometry of the complex de Sitter space-time and on the introduction of a class of holomorphic functions on this manifold, called perikernels, which reproduce mutatis mutandis the structural properties of the two-point correlation functions of the Minkowskian quantum field theory. The theory contains as basic elementary case the linear massive field models in their “preferred” representation. The latter are described by the introduction of de Sitter plane waves in their tube domains which lead to a new integral representation of the two-point functions and to a Fourier-Laplace type transformation on the hyperboloid. The Hilbert space structure of these theories is then analysed by using this transformation. In particular we show the Reeh-Schlieder property. For general two-point functions, a substitute to the Wick rotation is defined both in complex space-time and in the complex mass variable, and substantial results concerning the derivation of Källen-Lehmann type representation are obtained.