Related papers: Zero modes' fusion ring and braid group representa…
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…
The quantization of the chiral Schwinger model $(\chi QED_{2})$ with one-parameter class Faddeevian regularization is hampered by the chiral anomaly, i.e., the Gauss law commutator exhibits Faddeev's anomaly. To overcome this kind of…
We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…
Let $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ be the restricted integral form of the quantum loop algebra $U_q(L\mathfrak{sl}_2)$ specialised at a root of unity $\varepsilon$. We prove that the Grothendieck ring of a tensor…
Higher spin extensions of nonabelian gauge symmetries for both free fermionic model and WZNW model are considered on a classical level. It is characteristic property of the WZNW model that the higher spin currents which correspond to linear…
Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice ${\ee Z}_{D} \times {\ee Z}_{D}$ with specific emphasis on the deformed oscillator subalgebras and the generalized representations…
We prove the following result related to the inverse problem for universal deformation rings of group representations: Given a finite field k, denote by W(k) the ring of Witt vectors over k and by K the field of fractions of W(k). If a…
In this text, we study derived versions of the fusion category associated to Lusztig's quantum group $\textbf{U}_q$. The categories that so arise are non-semisimple but recovers the usual fusion ring when passing to complexified…
The conformal field theory based on the $g/u(1)^d$ coset construction is treated as the WZNW theory for the affine Lie algebra $\hat g$ with the constrained $\hat u(1)^d$ subalgebra.Using a modification of the generalized canonical…
This paper is the second part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey…
We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it…
We study the topological heterotic ring in (0,2) Landau-Ginzburg models without a (2,2) locus. The ring elements correspond to elements of the Koszul cohomology groups associated to a zero-dimensional ideal in a polynomial ring, and the…
We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to…
In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of…
We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems.…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in…
We study 2d $SU(N)$ QCD with an adjoint Dirac fermion. Assuming that the IR limit of the massless theory is captured by a WZW coset CFT, we show that this CFT can be decomposed into a sum of distinct CFTs, each representing a superselection…
The group $\GL_2$ over a local field with (residue) characteristic $2$ possesses much more smooth supercuspidal $\ell$-adic representations, than over a local field of residue characteristic $> 2$. One way to construct these representations…
We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to…