Related papers: Conformal, Integrable and Topological Theories, Gr…
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.
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
We use the AdS/CFT correspondence to study flows of N=4 SYM to non-conformal theories. The dual geometries can be seen as sourced by a Wigner's semicircle distribution of D3 branes. We consider two cases, the first case corresponds to a…
We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation…
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.
We find non-rational conformal field theories in two dimensions, which are solvable due to their correlators being related to correlators of Liouville theory. Their symmetry algebra consists of the dimension-two stress-energy tensor, and…
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.…
We investigate the mathematical structure of the world sheet in two-dimensional conformal field theories.
The paper aims to point out a novel geometric characterisation of the WDVV equations of 2D topological field theory.
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…
Conformal fields are a new class of $Vect(N)$ modules which are more general than tensor fields. The corresponding diffeomorphism group action is constructed. Conformal fields are thus invariantly defined.
In these notes I briefly outline SL(2) degenerate conformal field theories and their application to some related models, namely 2d gravity and N=2 discrete superconformal series.
Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
This is a brief introduction to the subject of Conformal Field Theory on surfaces with boundaries and crosscaps, which describes the perturbative expansion of open string theory.
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with locally solid topologies. Building upon the theory of…
We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one…