Related papers: Logarithmic ^sl(2) CFT models from Nichols algebra…

The most basic structure of chiral conformal field theory (CFT) is the Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the CFT's associated to loop groups, as twisted equivariant K-theory. We build on their work to…

These are lecture notes for an introductory course on Nichols algebras. As a main reference, I work with the book by Heckenberger and Schneider, but I want to take a distinct categorical perspective and try to develop the topic for an…

Instead of the Ginsparg-Wilson relation only generalized chiral symmetry is required. The resulting much larger class of Dirac operators for massless fermions is investigated and a general construction for them is given. It is also shown…

Inspired by 5d supersymmetric Yang-Mills theories placed on the compact space $\mathbb{S}^5$, we propose an intriguing algebraic construction for the $q$-Virasoro algebra. We show that, when multiple $q$-Virasoro "chiral" sectors have to be…

A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a…

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factorizing models)…

Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…

We construct the $Z_{N}$ symmetry extended fusion ring of bulk and chiral theories and the corresponding modular partition functions with nonanomalous subgroup $Z_{n}(\subset Z_{N})$. The chiral fusion ring provides fundamental data for…

We use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating funtions), which count gauge invariant operators in N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1 adjoint…

This paper is a first step toward the full description of a family of Hopf algebras whose coradical is isomorphic to a semisimple Hopf algebra K_{n}, n an odd positive integer, obtained by a cocentral abelian cleft extension. We describe…

An explicit check of the AGT relation between the W_N-symmetry controlled conformal blocks and U(N) Nekrasov functions requires knowledge of the Shapovalov matrix and various triple correlators for W-algebra descendants. We collect simplest…

We classify finite-dimensional pointed Hopf algebras with abelian coradical, up to isomorphism, and show that they are cocycle deformations of the associated graded Hopf algebra. More generally, for any braided vector space of diagonal type…

It was suggested recently that the study of 1-dimensional QCD with fermions in the adjoint representation could lead to an interesting toy model for strange metals and their holographic formulation. In the high density regime, the infrared…

I review the main features of the effective field theory (EFT) behind scenarios of dynamical electroweak symmetry breaking, placing particular emphasis on the systematics and the parallels that can be drawn with Chiral Perturbation Theory.…

We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero-Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at…

We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a…

This paper is a continuation of the paper entitled "Subshifts, $\lambda$-graph bisystems and $C^*$-algebras", arXiv:1904.06464. A $\lambda$-graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying certain compatibility…

We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case $\cg=S\ell(n)$, the existence of a suitable gauge, called Generalized…