N=2\ $W$-supergravity

TL;DR

This paper quantizes N=2 w_infinity supergravity, demonstrating how its algebra deforms into a super W_infinity algebra, and explores implications for quantum N=2 W_N supergravity with finite higher-spin symmetries.

Contribution

It provides a quantization of N=2 w_infinity supergravity and details the algebraic deformation to super W_infinity, connecting to finite higher-spin supergravity theories.

Findings

Deformation of N=2 super-w_infinity algebra into super-W_infinity algebra.

Extraction of quantum N=2 W_N supergravity structures from the algebraic framework.

Discussion of the specific case of quantum N=2 W_3 supergravity.

Abstract

We quantise the classical gauge theory of $N=2\ w_\infty$-supergravity and show how the underlying $N=2$ super-$w_\infty$ algebra gets deformed into an $N=2$ super-$W_\infty$ algebra. Both algebras contain the $N=2$ super-Virasoro algebra as a subalgebra. We discuss how one can extract from these results information about quantum $N=2\ W_N$-supergravity theories containing a finite number of higher-spin symmetries with superspin $s\le N$. As an example we discuss the case of quantum $N=2\ W_3$-supergravity.