Related papers: Parafermionic Reductions of WZW Model
This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak…
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the…
The four different kinds of currents are given by the multiple $(\beta,\gamma)$ and $(b,c)$ ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation…
We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet…
We introduce a generalization of $A_{r}$-type Toda theory based on a non-abelian group G, which we call the $(A_{r},G)$-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In…
We present a pure Chern-Simons formulation of families of interesting Conformal Field Theories describing edge states of non-Abelian Quantum Hall states. These theories contain two Abelian Chern-Simons fields describing the…
Parafermions modes are non-Abelian anyons which were introduced as $\mathbb{Z}_N$ generalizations of $\mathbb{Z}_2$ Majorana states. In particular, $\mathbb{Z}_3$ parafermions can be used to produce Fibonacci anyons, laying a path towards…
A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua…
Topological quantum computation relies on a protected degenerate subspace enabling complicated operations in a noise-resilient way. To this end, hybrid platforms based on non-Abelian quasiparticles such as parafermions hold great promise.…
We present the extension of the Wakimoto construction to the $su(2)_k$ quantum current algebra and its associated $Z_k$ quantum parafermion algebra. This construction is achieved in terms of various deformations of three classical free…
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
The weak currents with respect to the diagonal neutral bosons $Z$,$Z^{\prime}$, and $Z^{\prime\prime}$ of a specific \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} gauge model are computed in detail for all the fermion families involved therein. Our…
We extend standard path-integral techniques of bosonization and duality to the setting of noncommutative geometry. We start by constructing the bosonization prescription for a free Dirac fermion living in the noncommutative plane…
We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian reduction. In other words: we examine possible non-standard reality conditions for non-abelian…
We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1 unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the spins 1/2, 2 bosonic…
We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is $\mathbb{Z}_2$. This includes $SU(N)$ gauge theories with matter in the (anti)symmetric and $N$ even, and $USp(2N)$…
The defining relations (triple relations) of n pairs of parafermion operators f_j^\pm (j=1,...,n) are known to coincide with a set of defining relations for the Lie algebra so(2n+1) in terms of 2n generators. With the common Hermiticity…
We discuss the $N=2$ super $W$ algebras from the hamiltonian reduction of affine Lie superalgebras $A(n|n-1)^{(1)}$ and $A(n|n)^{(1)}$. From the quantum hamiltonian reduction of $A(n|n-1)^{(1)}$ we get the free field realization of $N=2$…
We study a system of two Tomonaga-Luttinger models coupled by a small transverse hopping (a two-chain ladder). We use Abelian and non-Abelian bosonisation to show that the strong coupling regime at low energies can be described by an…