A Realization of N=1 ${\cal SW}(3/2,2)$ Algebras with Wolf Spaces

TL;DR

This paper constructs realizations of certain N=1 superconformal algebras using Wolf space coset models, deriving explicit fermionic currents and connecting to topological field theories.

Contribution

It provides a new realization of N=1 ${ m SW}(3/2,2)$ algebras via Wolf space cosets and derives explicit fermionic currents, linking algebraic structures to topological theories.

Findings

Realization of N=1 ${ m SW}(3/2,2)$ algebras with Wolf space cosets

Explicit expression for fermionic current with weight 5/2

Connection to topological conformal field theories

Abstract

We find out that some unitary minimal models of the N=1 ${\cal SW}(3/2,2)$ superconformal algebra can be realized as the level one coset models based on the Wolf spaces $SU(n)/(SU(n-2)\times SU(2))$. We obtain the expression of the fermionic current with the conformal weight 5/2 in the algebra. Then, these models are twisted to give the topological conformal field theories.