Related papers: Exceptional embeddings of $N=2$ minimal models
We show that the Lie potential on the minimal semisimple adjoint orbit $\mathcal{O}_n$ of $\mathfrak{sl}(n+1,\mathbb{C})$ coincides with toric potential on $T^*\mathbb P^{n}$. We then study the corresponding Landau-Ginzburg models in…
If super-Yang-Mills theory possesses the exact conformal invariance, there is an additional modular invariance under the change of the complex bare charge $\tau = \frac{\theta}{2\pi}+ \frac{4\pi\imath}{g^2}\longrightarrow -\frac{1}{\tau}$.…
Recent progress on the relation between asymmetric conformal field theories and vacua of gauged supergravities is reviewed. This includes an attempt to classify asymmetric Gepner models in 8D, 6D and 4D with at least eight supercharges, and…
We study superstring propagations on the Calabi-Yau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N=2 Landau-Ginzburg theory and Liouville theory. If…
We developed a unified framework based on a special (non-regular) embedding of the exceptional group $E_6$ in which the main stage of symmetry breaking chain realizes $E_6\to G(2) \times SU(3)_A$. The exceptional factor $G(2)$ plays the…
We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and…
We review E$_{6(6)}$ exceptional field theory with a particular emphasis on the embedding of type IIB supergravity, which is obtained by picking the GL$(5)\times {\rm SL}(2)$ invariant solution of the section constraint. We work out the…
This paper addresses a conjecture of Kadison and Kastler that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N and, moreover, the implementing unitary can be chosen…
In this paper, we extend the results of Grantcharov and Robitaille in 2021 on mixed tensor products and Capelli determinants to the superalgebra setting. Specifically, we construct a family of superalgebra homomorphisms $\varphi_R :…
In this paper we consider the representation theory of N=1 Super-W-algebras with two generators for conformal dimension of the additional superprimary field between two and six. In the superminimal case our results coincide with the…
We prove a $\Gamma$-convergence result for a class of Ginzburg-Landau type functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is a closed and $(k-2)$-connected submanifold of $\mathbb{R}^m$, in arbitrary dimension. This…
We begin with a discussion on two apparently disconnected topics - one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G_2-manifold evaluated by the…
Kirchberg's Embedding Problem (KEP) asks whether every separable C$^*$ algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In this paper, we use model theory to show that this conjecture is equivalent to a local…
We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau…
Witten recently gave further evidence for the conjectured relationship between the $A$ series of the $N=2$ minimal models and certain Landau-Ginzburg models by computing the elliptic genus for the latter. The results agree with those of the…
We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the…
For any non-degenerate, quasi-homogeneous hypersurface singularity W and an admissible group of diagonal symmetries G, Fan, Jarvis, and Ruan have constructed a cohomological field theory which is a candidate for the mathematical structure…
Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…
For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a…
The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework…