Related papers: New maverick coset theories
In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
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…
It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…
We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable us to study a more general case. Various properties of the model such as OPEs, central charge,…
In this work we introduce new scalar field models and study the defect solutions they may engender. The investigation is based on the deformation procedure, which greatly simplify the calculations, leading us to new models together with the…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
A review of Word Embedding Models through a deconstructive approach reveals their several shortcomings and inconsistencies. These include instability of the vector representations, a distorted analogical reasoning, geometric incompatibility…
We extend the superembedding formalism for 4D N=1 superconformal field theory (SCFT) to the case of fields in arbitrary representations of the superconformal group SU(2,2|1). As applications we obtain manifestly superconformally covariant…
The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new…
This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…
We study the logarithmic conformal field theories in which conformal weights are continuous subset of real numbers. A general relation between the correlators consisting of logarithmic fields and those consisting of ordinary conformal…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the…