Related papers: Superconformal Coset Equivalence from Level-Rank D…
We propose new strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten's cigar model described by the $\mathfrak{sl}(2)/\mathfrak{u}(1)$ coset and…
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and…
A Supersymmetric Grand unified model is constructed based on SO(10)xSO(10) symmetry in which new types of Yukawa matrices couple standard and exotic fermions. Evolution of these couplings from the Grand Unified scale to the electroweak…
We investigate boundary states of N=2 coset models based on Grassmannians Gr(n,n+k), and find that the underlying intersection geometry is given by the fusion ring of U(n). This is isomorphic to the quantum cohomology ring of Gr(n,n+k+1),…
The large level limit of the $\mathcal{N}=2$ ${\rm SO}(2N)$ Kazama-Suzuki coset models is argued to be equivalent to the orbifold of $4N$ free fermions and bosons by the Lie group ${\rm SO}(2N) \times {\rm SO}(2)$. In particular, it is…
We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although this result is in principle known, the…
We present a derivation of the N=1 and N=2 superconformal coset constructions starting from a supersymmetric WZW model where a diagonal subgroup has been gauged. We work in the general framework of self-dual (not necessarily reductive) Lie…
A Lagrangian definition of a large family of (0,2) supersymmetric conformal field theories may be made by an appropriate gauge invariant combination of a gauged Wess-Zumino-Witten model, right-moving supersymmetry fermions, and left-moving…
In this paper, we prove a class of nontrivial q-Pochhammer symbol identities with extra parameters by iterated residue method. Then we use these identities to find relations of the quasi-map $K$-theoretical $I$-functions with level…
We argue that the discovery of neutrino mass effects at Super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed Minimal Left Right Supersymmetric models with a…
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodchikov equations constructed earlier by the second and third…
We study the representation theory of the Kazama-Suzuki coset vertex operator superalgebra associated with the pair of a complex simple Lie algebra and its Cartan subalgebra. In the case of type $A_{1}$, B.L. Feigin, A.M. Semikhatov, and…
In the context of the Grand Unified MSSM, we investigate the fermion mass matrices at GUT scale. We note that from the experimental mass pattern the determinants of the Yukawa matrices at this scale can be unified with good precision.…
We study the phases and fixed-point structure of two-dimensional supersymmetric Wess-Zumino models with one supercharge. Our work is based on the functional renormalization group formulated in terms of a manifestly off-shell supersymmetric…
A large class of two-dimensional $\mathcal{N}=(2,2)$ superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg…
We investigate the quantum behaviour of sigma models on coset superspaces G/H defined by Z_{2n} gradings of G. We find that, whenever G has vanishing Killing form, there is a choice of WZ term which renders the model quantum conformal, at…
The fractional level models are (logarithmic) conformal field theories associated with affine Kac-Moody (super)algebras at certain levels $k \in \mathbb{Q}$. They are particularly noteworthy because of several longstanding difficulties that…
We study supersymmetric unified models with three fermion generations based on the gauge group $SO(10)$ and require Gauge-Yukawa Unification, i.e., a renormalization group invariant functional relationship among the gauge and Yukawa…
We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$.…
We prove Feigin-Frenkel type dualities between subregular W-algebras of type A, B and principal W-superalgebras of type $\mathfrak{sl}(1|n), \mathfrak{osp}(2|2n)$. The type A case proves a conjecture of Feigin and Semikhatov. Let…