On partially formal supermanifolds

TL;DR

This paper introduces partially formal supermanifolds with mixed nilpotent and non-nilpotent coordinates, providing a framework to formulate superconformal field theories with varying supersymmetries in different sectors.

Contribution

It defines a new class of supermanifolds with mixed coordinate types, enabling novel formulations of superconformal field theories with asymmetric supersymmetries.

Findings

Defined finite-dimensional partially formal supermanifolds.

Showed their application in superconformal field theories.

Facilitated modeling of different supersymmetries in holomorphic and antiholomorphic sectors.

Abstract

We define a finite-dimensional partially formal supermanifold as a manifold having $q$ odd coordinates and $k + l$ even coordinates with $l$ of them taking only nilpotent values. We show that this notion can be used to formulate superconformal field theories with different numbers of supersymmetries in holomorphic and antiholomorphic sectors.