Symplectic fermions and a quasi-Hopf algebra structure on Uˉisl(2)\bar{U}_i sl(2)

We consider the (finite-dimensional) small quantum group $\bar{U}_q sl(2)$ at $q=i$. We show that $\bar{U}_i sl(2)$ does not allow for an R-matrix, even though $U \otimes V \cong V \otimes U$ holds for all finite-dimensional representations $U,V$ of $\bar{U}_i sl(2)$. We then give an explicit coassociator $\Phi$ and an R-matrix $R$ such that $\bar{U}_i sl(2)$ becomes a quasi-triangular quasi-Hopf algebra. Our construction is motivated by the two-dimensional chiral conformal field theory of symplectic fermions with central charge $c=-2$. There, a braided monoidal category, $\mathcal{SF}$, has been computed from the factorisation and monodromy properties of conformal blocks, and we prove that $\mathrm{Rep}\,(\bar{U}_i sl(2),\Phi,R)$ is braided monoidally equivalent to $\mathcal{SF}$.Comment: 40pp, 11 figures; v2: few very minor corrections for the final version in Journal of Algebr

An algorithm for twisted fusion rules

We present an algorithm for an efficient calculation of the fusion rules of twisted representations of untwisted affine Lie algebras. These fusion rules appear in WZW orbifold theories and as annulus coefficients in boundary WZW theories; they provide NIM-reps of the WZW fusion rules.Comment: 8 page

A non-rational CFT with c=1 as a limit of minimal models

We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the free boson but bears some resemblance to Liouville theory. Explicit expressions for the three point functions of bulk fields are presented, as well as a set of conformal boundary states. We provide analytic and numerical arguments in support of the claim that this data forms a consistent CFT.Comment: latex2e, 37 pages, 4 figure

N=2 minimal conformal field theories and matrix bifactorisations of x^d

We establish an action of the representations of N=2-superconformal symmetry on the category of matrix factorisations of the potentials x^d and x^d-y^d for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu–Schwarz-type representa-tions of the N = 2 minimal super vertex operator algebra at central charge 3–6/d, and (b) a full subcategory of graded matrix factorisations of the potential x^d − y^d . The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. The physical motivation for this result is the Landau–Ginzburg/conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [BR], where an isomorphism of fusion rules was established

Conformal boundary conditions and 3D topological field theory

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.Comment: 10 pages, 2 figures. Invited talk by C.S. at the NATO Advanced Research Workshop on Statistical Field Theories, Como, June 200

Finite size effects in perturbed boundary conformal field theories

We discuss the finite-size properties of a simple integrable quantum field theory in 1+1 dimensions with non-trivial boundary conditions. Novel off-critical identities between cylinder partition functions of models with differing boundary conditions are derived.Comment: 7 pages, 11 figures, JHEP proceedings style. Uses epsfig, amssymb. Talk given at the conference `Nonperturbative Quantum Effects 2000', Pari

Superconformal defects in the tricritical Ising model

We study superconformal defect lines in the tricritical Ising model in 2 dimensions. By the folding trick, a superconformal defect is mapped to a superconformal boundary of the N=1 superconformal unitary minimal model of c=7/5 with D_6-E_6 modular invariant. It turns out that the complete set of the boundary states of c=7/5 D_6-E_6 model cannot be interpreted as the consistent set of superconformal defects in the tricritical Ising model since it does not contain the "no defect" boundary state. Instead, we find a set of 18 consistent superconformal defects including "no defect" and satisfying the Cardy condition. This set also includes some defects which are not purely transmissive or purely reflective.Comment: 25 pages, 3 figures. v2: typos corrected. v3: clarification about spin structure aligned theory added, references adde

Defect flows in minimal models

In this paper we study a simple example of a two-parameter space of renormalisation group flows of defects in Virasoro minimal models. We use a combination of exact results, perturbation theory and the truncated conformal space approach to search for fixed points and investigate their nature. For the Ising model, we confirm the recent results of Fendley et al. In the case of central charge close to one, we find six fixed points, five of which we can identify in terms of known defects and one of which we conjecture is a new non-trivial conformal defect. We also include several new results on exact properties of perturbed defects and on the renormalisation group in the truncated conformal space approach.Comment: 35 pages, 21 figures. 1 reference adde