Related papers: Central functions and their physical implications
This thesis is dedicated to analysing the general structure of two- and three-point correlation functions of conserved currents of arbitrary integer or half-integer spins in three- and four-dimensional (super)conformal field theory.
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
Conformal symmetry has important consequences for strong interactions at short distances and provides powerful tools for practical calculations. Even if the Lagrangians of Quantum Chromodynamics (QCD) and Electrodynamics (QED) are invariant…
A hierarchy of effective field theories is used to separate the contributions from different momentum scales and to calculate the free energy of QCD at high temperature in powers of the coupling constant up to order $g^5$. The behavior of…
Two dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges, built out of the stress tensor. We compute the thermal correlation functions of the these KdV charges on a circle. We show that…
Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is…
Several pieces of evidence have been recently brought up in favour of the c-theorem in four and higher dimensions, but a solid proof is still lacking. We present two basic results which could be useful for this search: i) the values of the…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…
I discuss the possibility of using classical field theory to approximate hot, real-time quantum field theory. I calculate, in a scalar theory, the classical two point and four point function in perturbation theory. The counterterms needed…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that…
Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds in particular…
We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…
Understanding the link between correlation functions (CFs) of local operators and measurable collider correlators has emerged as a new opportunity in the study of gauge theory dynamics at colliders. While in Conformal Field Theories (CFTs)…
We compute holographic one- and two-point functions of critical higher-curvature gravity in four dimensions. The two most important operators are the stress tensor and its logarithmic partner, sourced by ordinary massless and by logarithmic…
The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate…
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…
The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as…
Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…