Related papers: On Affine Fusion and the Phase Model
The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affine Lie algebra) of the WZW model, while the Einstein equations of the general non-linear…
Recently, properties of collective states of interacting non-abelian anyons have attracted a considerable attention. We study an extension of the `golden chain model', where two- and three-body interactions are competing. Upon fine-tuning…
Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated…
The parabolic category $\mathcal{O}$ for affine ${\mathfrak{gl}}_N$ at level $-N-e$ admits a structure of a categorical representation of $\widetilde{\mathfrak{sl}}_e$ with respect to some endofunctors $E$ and $F$. This category contains a…
A dynamical system is canonically associated to every Drinfeld double of any affine Kac-Moody group. The choice of the affine Lu-Weinstein-Soibelman double gives a smooth one-parameter deformation of the standard WZW model. In particular,…
In this paper, we study the convolution structure in the special affine Fourier transform domain to combine the advantages of the well known special affine Fourier and Stockwell transforms into a novel integral transform coined as special…
Some WZW models on affine Lie superalgebras at critical level describe string theory on AdS backgrounds at critical values of the string tension. This is the case of $\mathfrak{psu}(1,1|2)_1$ for ${\rm AdS}_3 \times {\rm S}^3$ and…
In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik-Okounkov $R$-matrix. We discuss the relation between $RLL$ and current realization of the affine Yangian of…
Let $G$ be a connected reductive group over an algebraically closed field $k$, and let $Fl$ be the affine flag variety of $G$. For every regular semisimple element $\gamma$ of $G(k((t)))$, the affine Springer fiber $Fl_{\gamma}$ can be…
We construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases. The construction is based…
The color excitations of interacting fermions carrying an $SU(3)$ color and $U(N_f)$ flavor index in one spatial dimension are studied in the framework of a perturbed $SU(3)_{N_f}$ Wess-Zumino-Novikov-Witten model. Using Bethe ansatz…
We invistigate exact solutions for the two-dimensional quantum field theories called Wess-Zumino-Novikov-Witten (WZNW) models. A WZNW model is a sigma model whose classical fields are applications from a bidimensional space-time (a Riemann…
Binary mixtures of lamellar colloids represented by hard platelets are studied within a generalization of the Zwanzig model for rods, whereby the square cuboids can take only three orientations along the $x$, $y$ or $z$ axes. The free…
We shall give an axiomatic construction of Wess-Zumino-Witten actions valued in (G=SU(N)), (N\geq 3). It is realized as a functor ({WZ}) from the category of conformally flat four-dimensional manifolds to the category of line bundles with…
Vafa-Witten (VW) theory is a topologically twisted version of N=4 supersymmetric Yang-Mills theory. S-duality suggests that the partition function of VW theory with gauge group SU(N) transforms as a modular form under duality…
The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…
It was proposed a flavour model based on the symmetry group S4, managing to describe fermion masses and mixings. The Weinberg operator has been used in order to provide the smallness of the neutrino masses, while a set of scalar fields,…
The affine Schur algebra $\widetilde{S}(n,r)$ (of type A) over a field $K$ is defined to be the endomorphism algebra of the tensor space over the extended affine Weyl group of type $A_{r-1}$. By the affine Schur-Weyl duality it is…
A method of computing fusion coefficients for Lie algebras of type $A_{n-1}$ on level $k$ was recently developed by A. Feingold and M. Weiner \cite{FW} using orbits of $\mathbb{Z}_n^k$ under the permutation action of $S_k$ on $k$-tuples.…