Related papers: The world sheet revisited
The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…
A world sheet in Lorentz-Minkowski space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds in Lorentz-Minkowski space. In this paper we investigate differential geometry of world sheets in…
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter,…
In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…
We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two…
The ADE classification scheme is encountered in many areas of mathematics, most notably in the study of Lie algebras. Here such a scheme is shown to describe families of two-dimensional conformal field theories.
We review conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry.…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma…
Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…
We study maps from a 2D world-sheet to a 2D target space which include folds. The geometry of folds is discussed and a metric on the space of folded maps is written down. We show that the latter is not invariant under area preserving…
This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but…
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.
In this paper we study one-dimensional conformal field theory at finite temperature dual to the two-dimensional anti-de Sitter spacetime in the Rindler coordinates. We show that conformal symmetry for thermal two-point functions manifests…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
We discuss the geometry behind some integrals related to structure constants of the Liouville conformal field theory.
Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two…
We discuss some global and semi-global existence and stability results obtained with the use of the conformal field equations.
The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.