Related papers: Adding Complex Fermions to the Grassmannian-like C…
The large ${\cal N}=4$ nonlinear superconformal algebra is generated by six spin-$1$ currents, four spin-$\frac{3}{2}$ currents and one spin-$2$ current. The simplest extension of these $11$ currents is described by the $16$ higher spin…
By calculating the second order pole in the operator product expansion (OPE) of the charged spin-$3$ current with the neutral spin-$3$ current in the Grassmannian-like coset model, we determine the primary charged spin-$4$ current.…
We discuss the nonlinear extension of $N=2$ superconformal algebra by generalizing Sugawara construction and coset construction built from $N=2$ currents based on Kazama-Suzuki $N=2$ coset model $\frac{SU(3)}{SU(2) \times U(1)}$ in $N=2$…
Extended supersymmetric sigma-model is given, standing on the SO(2N+1) Lie algebra of fermion operators composed of annihilation-creation operators and pair operators. Canonical transformation, the extension of the SO(2N) Bogoliubov…
We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (\alpha_{1} \alpha_{2} \alpha_{3} \alpha_{4}) }$ which we refer to as the superspin-2 current multiplet.…
The large N=4 linear superconformal algebra (generated by four spin-1/2 currents, seven spin-1 currents, four spin-3/2 currents and one spin-2 current) found by Sevrin, Troost and Van Proeyen (and other groups) was realized in the N=4…
We study the strong coupling behaviour of null polygonal Wilson loops/gluon amplitudes in $\mathcal{N} = 4$ SYM, by using the OPE series and its integrability features. For the hexagon we disentangle the $SU(4)$ matrix structure of the form…
Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments…
General fermionic expressions for the branching functions of the rational coset conformal field theories $\widehat{su}(2)_{M}\times \widehat{su}(2)_N/\widehat{su}(2)_{M+N}$ are given. The equality of the bosonic and fermionic…
We construct an off-shell $\mathcal{N}=2$ superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin ${\bf s}$ gauge $\mathcal{N}=2$ supermultiplet % in flatfour-dimensional space. in a general…
We investigate the possibility to construct extended parafermionic conformal algebras whose generating current has spin $1+\frac{1}{K}$, generalizing the superconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras. Models…
By using the known operator product expansions (OPEs) between the lowest $16$ higher spin currents of spins $(1, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}, 2,2,2,2,2,2, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, 3)$ in an…
We quantize the one-particle model of the ${\rm SU}(2|1)$ supersymmetric multi-particle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as…
We study a $SU(2)$-symmetric spin-${3}/{2}$ system on a bipartite lattice close to the antiferromagnetic $SU(4)$-symmetric point, which can be described by the $CP^{3}$ model with a perturbation breaking the symmetry from $SU(4)$ down to…
We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum…
We build a supersymmetric model with $SU(2)_{L}\otimes SU(2)_{R}\otimes U(1)_{(B-L)}$ electroweak gauge symmetry, where $SU(2)_{L}$ is the left-handed currents while $SU(2)_{R}$ is the right-handed currents and $B$ and $L$ are the usual…
By using the $K$-free complex bosons and the $K$-free complex fermions, we construct the ${\cal N}=2$ supersymmetric $W_{\infty}^{K,K}$ algebra which is the matrix generalization of previous ${\cal N}=2$ supersymmetric $W_{\infty}$ algebra.…
It is known that the unitary representation of the D=4, N=4 superconformal multiplets and their descendants are constructed as supercoherent states of bosonic and fermionic creation oscillators which covariantly transform under SU(2,2|4).…
Strongly disordered spin chains invariant under the SO(N) group are shown to display random-singlet phases with emergent SU(N) symmetry without fine tuning. The phases with emergent SU(N) symmetry are of two kinds: one has a ground state…
We study the holographic duality between the M x M matrix extension of Vasiliev higher spin theories on AdS3 and the large N limit of SU(N+M)/SU(N) x U(1) type cosets. We present a simplified proof for the agreement of the spectra and…