# Semi-conformal structure on certain vertex superalgebras associated to vertex superalgebroids

## TL;DR

This paper introduces a new class of vertex superalgebras linked to vertex superalgebroids, characterizes when they are semi-conformal, and provides explicit examples and applications.

## Contribution

It defines vertex superalgebroids, constructs associated vertex superalgebras, and establishes necessary and sufficient conditions for their semi-conformal structure.

## Key findings

- Identified conditions for semi-conformality of vertex superalgebras
- Constructed explicit examples of semi-conformal vertex superalgebras
- Applied theoretical results to specific superalgebra cases

## Abstract

In this paper, we first give the definiton of a vertex superalgebroid. Then we construct a family of vertex superalgebras associated to vertex superalgebroids. As a main result, we find a sufficient and necessary condition that this vertex superalgebras are semi-conformal. In addition, we give an concrete example of this vertex superalgebras and apply our results to this superalgebra.