Related papers: NSR singular vectors from Uglov polynomials
We propose an exact form of the fusion matrix of the Neveu-Schwarz blocks that appear in a correlation function of four super-primary fields. Orthogonality relation satisfied by this matrix is equivalent to the bootstrap equation for the…
Using a superspace representation of the N=3 Neveau-Schwarz super Virasoro algebra, we find solutions of N=3 super Ward identities. Global transformations generated by the non-abelian supercurrent require not only superfields, but also…
We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and…
We study the representation theory of the N=1 super Heisenberg-Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg-Virasoro vertex algebra arXiv:math/0201314, arXiv:1405.1707 and arXiv:1703.00531 to the…
The N=1 Volkov-Akulov model of nonlinear supersymmetry is explicitly related to a vector supermultiplet model with a Fayet-Iliopoulos D term of linear supersymmetry. The physical significance of the results is discussed briefly.
The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial…
We prove the connection between the Nekrasov partition function of N=2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations.…
A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald…
We classify the supersymmetric solutions of ungauged N=1 d=5 SUGRA coupled to vector multiplets and hypermultiplets. All the solutions can be seen as deformations of solutions with frozen hyperscalars. We show explicitly how the…
In this paper we propose a resolution to the problem of $\beta$-deforming the non-Gaussian monomial matrix models. The naive guess of substituting Schur polynomials with Jack polynomials does not work in that case, therefore, we are forced…
We derive properties of N-extended GR super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification…
This note shows that the orbifold Jacobian algebra associated to each invertible polynomial defining an exceptional unimodal singularity is isomorphic to the (usual) Jacobian algebra of the Berglund-H\"{u}bsch transform of an invertible…
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras.…
A general construction is found for `topological' singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for sl(2) singular vectors due to Malikov--Feigin--Fuchs, but is…
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters…
In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor…
We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and $16 + 16$ types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains…
We give a survey on results related to the Berglund-H\"ubsch duality of invertible polynomials and the homological mirror symmetry conjecture for singularities.
This paper develops a theory of isolated hypersurface singularities in mixed characteristic $(0,p)$, focusing on quotient rings over a Discrete Valuation Ring (DVR). We introduce and study analogues of the classical Tjurina and Milnor…
We investigate bosonic sectors of supersymmetric field theories. We consider superpotentials described by one and by two real scalar fields, and we show how the equations of motion can be factorized into a family of first order Bogomol'nyi…