Related papers: $N=4$ superconformal algebras and diagonal cosets
We show that four-dimensional superconformal algebras admit an infinite-dimensional derived enhancement after performing a holomorphic twist. The type of higher symmetry algebras we find are closely related to algebras studied by…
The class of 2d minimal model CFTs with higher spin AdS3 duals is extended to theories with large N=4 superconformal symmetry. We construct a higher spin theory based on the global D(2,1|alpha) superalgebra, and propose a large N family of…
We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…
We give an explicit description for the weight three generator of the coset vertex operator algebra $C_{L_{\widehat{\sl_{n}}}(l,0)\otimes L_{\widehat{\sl_{n}}}(1,0)}(L_{\widehat{\sl_{n}}}(l+1,0))$, for $n\geq 2, l\geq 1$. Furthermore, we…
We study the representation theory of the superconformal algebra $W_k(g,f_{\theta})$ associated with a minimal gradation of $g$. Here, $g$ is a simple finite-dimensional Lie superalgebra with a non-degenerate, even supersymmetric invariant…
Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…
The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for $\mathcal{N}=3$, $D = 4$. The construction is based on a supersymmetry…
We classify all possible occurrences of Kazama-Suzuki duality between the ${N=2}$ superconformal algebra $L^{N=2}_c$ and the subregular $\mathcal{W}$-algebra $\mathcal{W}_{k}(\mathfrak{sl}_4, f_{\rm sub})$. We establish a new Kazama-Suzuki…
We review the construction of extended ( N=2 and N=4 ) superconformal algebras over triple systems and the gauged WZW models invariant under them. The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems (FTS) admit…
We show how three-dimensional superconformal theories for any number N <= 8 of supersymmetries can be obtained by taking a conformal limit of the corresponding three-dimensional gauged supergravity models. The superconformal theories are…
Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular $\mathcal{W}$-algebras and the principal $\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It can be…
In this note we study four dimensional theories with N=3 superconformal symmetry, that do not also have N=4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that…
We present a way of constructing string solutions around non-trivial gravitational backgrounds. The proposed solutions are constructed using $N = 4$ superconformal building blocks with $\hat c = 4$. We give two different and inequivalent…
For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS_3, the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the…
This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…
We examine rectangular W-algebras with $so(M)$ or $sp(2M)$ symmetry, which can be realized as the asymptotic symmetry of higher spin gravities with restricted matrix extensions. We compute the central charges of the algebras and the levels…
Starting from superdifferential operators in an $N=1$ superfield formulation, we present a systematic prescription for the derivation of classical $N=1$ and $N=2$ super W-algebras by imposing a zero-curvature condition on the connection of…
We give an introduction to conformal and superconformal algebras and their representations in various dimensions. Special emphasis is put on 4d $\mathcal{N}=2$ superconformal symmetry. This is the writeup of the lectures given at the Winter…
When W is a finite Coxeter group of classical type (A, B, or D), noncrossing partitions associated to W and compatibility of almost positive roots in the associated root system are known to be modeled by certain planar diagrams. We show how…
We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex…