New fields on super Riemann surfaces

TL;DR

This paper introduces a novel super vector bundle on super Riemann surfaces, leading to a new class of fields with stable dimensional properties, advancing the understanding of supergeometry and its applications.

Contribution

It describes a new (1,1)-dimensional super vector bundle on super Riemann surfaces and characterizes a new class of fields with fixed dimension properties.

Findings

Existence of a new super vector bundle on any super Riemann surface.

Introduction of a new class of fields resembling holomorphic functions.

These fields have a well-defined, stable dimension regardless of odd moduli.

Abstract

A new $(1,1)$-dimensional super vector bundle which exists on any super Riemann surface is described. Cross-sections of this bundle provide a new class of fields on a super Riemann surface which closely resemble holomorphic functions on a super Riemann surface, but which (in contrast to the case with holomorphic functions) form spaces which have a well defined dimension which does not change as odd moduli become non-zero.