Uhi Rinn Suh: N=2 primary superconformal structure of the classical SUSY W-algebra W(𝔰𝔩(n+1|n))

For a given pair of a simple finite basic Lie superalgebra and its odd nilpotent element, one can construct the corresponding N=1 SUSY vertex algebra called SUSY W-algebra. The structure of any SUSY W-algebra is quite complicated but SUSY W-algebra associated with 𝔰𝔩(n+1|n) and its odd principal nilpotent f_pr is relatively simple. In particular, 𝔰𝔩(n+1|n) is the only simple basic Lie superalgebra which admits principal 𝔰𝔩(2|1)-embedding and it gives rise to an N=2 primary superconformal structure of the classical SUSY W-algebra for 𝔰𝔩(n+1|n) and f_pr. In the first part of this talk, I will introduce the notions of quantum and classical SUSY W-algebra and their basic properties. In the second part, I will explain the recent result on N=2 primary superconformal superconformal structure of the classical SUSY W-algebra associated with 𝔰𝔩(n+1|n) and f_pr.

This presentation is mainly based on the joint work with Ragoucy and Song, and based on this arXiv paper.

This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Geometric Representation Theory and W-algebras.