Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves

TL;DR

This paper develops a mathematical framework for D-strings as morphisms from Azumaya prestable curves with a fundamental module to a target variety, aiming to formalize topological D-string instantons within string theory.

Contribution

It constructs the moduli stack of such morphisms, providing a foundational step towards a rigorous mathematical theory of topological D-strings and their instantons.

Findings

Defined the moduli stack of morphisms from Azumaya prestable curves to a fixed target.

Established a prototype for Wick-rotated D-strings of B-type on the target variety.

Laid groundwork for a mathematical theory of topological D-string world-sheet instantons.

Abstract

This is a continuation of our study of the foundations of D-branes from the viewpoint of Grothendieck in the region of the related Wilson's theory-space where "branes" are still branes. In this work, we focus on D-strings and construct the moduli stack of morphisms from Azumaya prestable curves $C^{Az}$ with a fundamental module ${\cal E}$ to a fixed target $Y$ of a given combinatorial type. Such a morphism gives a prototype for a Wick-rotated D-string of B-type on $Y$, following the Polchinski-Grothendieck Ansatz, and this stack serves as a ground toward a mathematical theory of topological D-string world-sheet instantons.