Related papers: A guide to two-dimensional conformal field theory
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
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…
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(\alpha,\beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…
I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrum-generating symmetries of classical string theory.
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…
The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures…
The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.
We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of…
We investigate second order conformal perturbation theory for $\mathbb{Z}_2$ orbifolds of conformal field theories in two dimensions. To evaluate the necessary twisted sector correlation functions and their integrals, we map them from the…
In this work, we propose an effective action of the two-dimensional conformal field theory for the Soft modes appearing in Quantum ElectroDynamics (QED) in 4 dimensions. This is motivated in two ways. First, we motivate the notion of an…
This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts.…
Auxiliary field techniques have recently gained interest in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. In these settings, coupling a suitable ``seed'' theory to auxiliary fields provides a…