Related papers: Extended su(2)_k and restricted U_q sl(2)
We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the…
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
We investigate dimensional constraints arising from representation theory when abstract graph edges possess internal degrees of freedom but lack geometric properties. We prove that such internal degrees of freedom can only encode…
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…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
We study fractional exclusion statistics for quantum systems with SU(2) symmetry (arbitrary spin $S$), by generalizing the thermodynamic equations with squeezed strings proposed by Ha and Haldane. The bare hole distributions as well as the…
We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In…
We study an extension of the Minimal Supersymmetric Standard Model with a gauge group $SU(2)_1\otimes SU(2)_2$ breaking to $SU(2)_L$. The extra wino has an enhanced gauge coupling to the SM-like Higgs boson and, if light, has a relevant…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
We study the Poisson bracket algebra of the $N=2$ supersymmetric chiral WZNW model in superspace. It involves two classical r-matrices, one of which comes from the geometrical constraints implied by $N=2$ supersymmetry. The phase space…
We compute the gauge field functional integral giving the scalar product of the SU(2) Chern-Simons theory states on a Riemann surface of genus > 1. The result allows to express the higher genera partition functions of the SU(2) WZNW…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
A popular way to study N=1 supersymmetric gauge theories is to realize them geometrically in string theory, as suspended brane constructions, D-branes wrapping cycles in Calabi-Yau manifolds, orbifolds, and otherwise. Among the applications…
We identify the quantum group ${\Large\textsl{U}}_\textsl{w}(sl_2)$ in the $L$-operator of $\tau^{(2)}$-model for a generic $\textsl{w}$ as a subalgebra of $U_{\sf q} (sl_2)$ with $\textsl{w} = {\sf q}^{-2}$. In the roots of unity case,…
We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the…
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than 4 dimensions, a SU(n) gauge theory on a Moyal-Weyl space arises with…
We critically look at Senthil Fisher constructions of quantum number fractionization in cuprates. The first construction, while mathematically correct is of limited relevance to cuprates. The second one has a missing local U(1) symmetry.…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…
N=2 three dimensional Supergravity with internal $R-$symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to…
The conventional supersymmetric grand unified theories suffer from two serious problems, the large mass splitting between doublet and triplet Higgs multiplets, and the too long lifetime of the proton. A unification model based on a…