Superconformal algebras and Lie superalgebras of the Hodge theory

TL;DR

This paper uncovers a correspondence between superconformal algebra zero modes and Lie superalgebras in K{"a}hler and hyper-K{"a}hler geometry, revealing new links between algebraic structures and geometric operators.

Contribution

It establishes a novel connection between superconformal algebra zero modes and classical geometric Lie superalgebras, expanding understanding of their interplay.

Findings

Identifies correspondence between superconformal algebra zero modes and geometric Lie superalgebras

Links algebraic structures to classical operators in K{"a}hler and hyper-K{"a}hler geometry

Provides a new perspective on the algebraic underpinnings of geometric operators

Abstract

We observe a correspondence between the zero modes of superconformal algebras $S'(2, 1)$ and W(4) and the Lie superalgebras formed by classical operators appearing in the K{\"a}hler and hyper-K{\"a}hler geometry.