# Supersymmetric W-algebras

@article{Molev2021SupersymmetricW, title={Supersymmetric W-algebras}, author={Alexander I. Molev and Eric Ragoucy and Uhi Rinn Suh}, journal={Letters in Mathematical Physics}, year={2021}, volume={111}, pages={1-25} }

We explain a general theory of W -algebras in the context of supersymmetric vertex algebras. We describe the structure of W -algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As an application, we produce explicit free generators of the W -algebra associated with the odd principal nilpotent element of the Lie superalgebra $$\mathfrak {gl}(n+1|n)$$ gl ( n + 1 | n ) .

## 5 Citations

### Generators of Supersymmetric Classical $W$-algebras

- Mathematics
- 2021

Let g be a Lie superalgebra of type sl or osp with an odd principal nilpotent element f . We consider a matrix Ag,f determined by g and f and find a generating set of the supersymmetric classical W…

### Dirac reductions and Classical W-algebras

- Mathematics
- 2022

. In the ﬁrst part of this paper, we generalize Dirac reduction to the extent of non-local Poisson vertex superalgebra and non-local SUSY Poisson vertex algebra cases. Next, we modify this reduction…

### 𝒲-Algebras Associated With Centralizers in Type A

- MathematicsInternational Mathematics Research Notices
- 2020

We introduce a new family of affine $\mathcal{W}$-algebras $\mathcal{W}^{k}(\mathfrak{a})$ associated with the centralizers of arbitrary nilpotent elements in $\mathfrak{gl}_N$. We define them by…

### Structures of (supersymmetric) classical W-algebras

- Mathematics
- 2020

In the first part of this paper, we discuss the classical W-algebra $\mathcal{W}(\mathfrak{g}, F)$ associated with a Lie superalgebra $\mathfrak{g}$ and the nilpotent element $F$ in an…

### Superconformal surfaces in four dimensions

- MathematicsJournal of High Energy Physics
- 2020

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the…

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