Related papers: Universal $2$-parameter $\mathcal{N}=2$ supersymme…

The universal $2$-parameter vertex algebra $W_{\infty}$ of type $W(2,3,4,\dots)$ serves as a classifying object for vertex algebras of type $W(2,3,\dots,N)$ for some $N$ in the sense that under mild hypothesis, all such vertex algebras…

We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by the weights $2$ and $3$ fields. Subject to…

There are three universal $2$-parameter vertex algebras $\mathcal{W}_{\infty}$, $\mathcal{W}^{\text{ev}}_{\infty}$, and $\mathcal{W}^{\mathfrak{sp}}_{\infty}$ which are freely generated of types $\mathcal{W}(2,3,4,\dots)$,…

We construct the unique two-parameter vertex algebra which is freely generated of type ${\mathcal W}(2,4,6,\dots)$, and generated by the weights $2$ and $4$ fields. Subject to some mild constraints, all vertex algebras of type ${\mathcal…

The universal two-parameter ${\mathcal W}_{\infty}$-algebra is a classifying object for vertex algebras of type ${\mathcal W}(2,3,\dots, N)$ for some $N$. Gaiotto and Rap\v{c}\'ak recently introduced a large family of such vertex algebras…

We prove the conjecture of Gaiotto and Rap\v{c}\'ak that the $Y$-algebras $Y_{L,M,N}[\psi]$ with one of the parameters $L,M,N$ zero, are simple one-parameter quotients of the universal two-parameter $\mathcal{W}_{1+\infty}$-algebra, and…

We identify the rank $(q_{syk}+1)$ of the interaction of the two-dimensional ${\cal N}=(2,2)$ SYK model with the deformation parameter $\lambda$ in the Bergshoeff, de Wit and Vasiliev(in 1991)'s linear $W_{\infty}[\lambda]$ algebra via…

Let $\mathfrak{g}$ be a basic Lie superalgebra and $f$ be an odd nilpotent element in an $\mathfrak{osp}(1|2)$ subalgebra of $\mathfrak{g}$. We provide a mathematical proof of the statement that the W-algebra $W^k(\mathfrak{g},F)$ for…

We describe an $N=2$ supersymmetric Poisson vertex algebra structure of $N=1$ (resp. $N=0$) classical $W$-algebra associated with $\mathfrak{sl}(n+1|n)$ and the odd (resp. even) principal nilpotent element. This $N=2$ supersymmetric…

To each complex reflection group $\Gamma$ one can attach a canonical symplectic singularity $\mathcal{M}_\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli…

We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional…

There is an embedding of affine vertex algebras $V^k(\mathfrak{gl}_n) \hookrightarrow V^k(\mathfrak{sl}_{n+1})$, and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n), V^k(\mathfrak{sl}_{n+1}))$ is a natural generalization of…

Trialities of $\mathcal{W}$-algebras are isomorphisms between the affine cosets of three different $\mathcal{W}$-(super)algebras, and were first conjectured in the physics literature by Gaiotto and Rap\v{c}\'ak. In this paper we prove…

$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…

The notion of "N = 2 vertex superalgebra with two odd formal variables" is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is incorporated into the usual Jacobi identity for a…

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in ${\cal N}=4$ Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of…

The affine Yangian of $\mathfrak{gl}_1$ is isomorphic to the universal enveloping algebra of $\mathcal{W}_{1+\infty}$ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family…

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1 unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the spins 1/2, 2 bosonic…

Using bootstrap methods, we provide evidence for the existence of a non-linear W-algebra, denoted $W_\infty^\text{s,s}$, which contains the small N= 4 super Virasoro algebra and features an infinite tower of additional generators, organized…