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

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 $\mathcal{E}$ 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.

30 pages

References in corpus (3)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
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• Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint