Related papers: The Capitulation Problem in Class Field Theory
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
This article surveys recent advances and future challenges in the $2$-representation theory of finitary $2$-categories with a particular emphasis on problems related to classification of various classes of $2$-representations.
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
This primer is an introduction to Conformal Field Theory in $D\geq3$. It is designed to introduce the reader to many of the important foundational concepts and methods in CFT. In it, pig picture ideas are prioritized over technical details,…
Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
We discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
These lectures review phases and phase transitions of the Standard Model, with emphasis on those aspects which are amenable to a first principle study. Model calculations and theoretical ideas of practical applicability are discussed as…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
An attempt of a new kind of complexity anthropology is considered.
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
The following 5 lectures are devoted to key ideas in field theory and in the Standard Model.