Related papers: Fixed Point Resolution in Extensions of Permutatio…
We find a formula for the resolution of fixed points in extensions of permutation orbifold conformal field theories by its (half-)integer spin simple currents. We show that the formula gives a unitary and modular invariant S matrix.
In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N=2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure…
A formula is derived for the fixed point resolution matrices of simple current extended WZW-models and coset conformal field theories. Unlike the analogous matrices for unextended WZW-models, these matrices are in general not symmetric, and…
We review extensions by integer spin simple currents in two-dimensional conformal field theories and their applications in string theory. In particular, we study the problem of resolving the fixed points of a simple current and apply the…
In the first of this two-part series, we find `fixed point factorisation' formulas, towards an understanding of the fusion ring of WZW models. Fixed-point factorisation refers to the simplifications in the data of a CFT involving primary…
A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points,…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
The conjecture of Fuchs, Schellekens and Schweigert on the relation of mapping class group representations and fixed point resolution in simple current extensions is investigated, and a cohomological interpretation of the untwisted…
Coupling $N$ large $m$ minimal models and flowing to IR fixed points is a systematic way to build new classes of compact unitary 2d CFTs which are likely to be irrational, and potentially have a positive Virasoro twist gap above the…
Some applications of simple current techniques and fixed point resolution to theories of open strings are discussed. In addition to a brief review of work presented in two recent papers with L. Huiszoon and N. Sousa, some new results…
We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the…
Through coarse-graining, tensor network representations of a two-dimensional critical lattice model flow to a universal four-leg tensor, corresponding to a conformal field theory (CFT) fixed-point. We computed explicit elements of the…
The question ''Which abelian permutation groups arise as group of simple currents in Rational Conformal Field Theory?'' is investigated using the formalism of weighted permutation actions. After a review of the relevant properties of simple…
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG…
In some CFT models of simple current type, which are used to describe string theory on orbifolds and (adjoint) cosets of Lie groups, there arise fixed points of the simple current group. In these cases, the standard procedure to associate…
We construct a generalization of the cyclic $\lambda$-deformed models of \cite{Georgiou:2017oly} by relaxing the requirement that all the WZW models should have the same level $k$. Our theories are integrable and flow from a single UV point…
An algebraic formulation of the stringy geometry on simple current orbifolds of the WZW models of type A_N is developed within the framework of Reflection Equation Algebras, REA_q(A_N). It is demonstrated that REA_q(A_N) has the same set of…
We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k…
We construct a class of 3-point constants in the $sl(4)$ Toda conformal theory $W_4$, extending the examples in Fateev and Litvinov. Their knowledge allows to determine the braiding/fusing matrix transforming 4-point conformal blocks of one…