Linear sigma model toolshed for D-brane physics

TL;DR

This paper develops linear sigma models for strings on curved spaces with branes, incorporating general gauge configurations and explaining the mathematical basis for worldsheet interactions, thus clarifying the role of derived categories in D-brane physics.

Contribution

It introduces a broad class of linear sigma models for D-branes on curved backgrounds, linking mathematical structures to physical string configurations.

Findings

Models include diverse brane-worldvolume gauge fields

Provides a mathematical framework for worldsheet interactions

Clarifies the role of derived categories in D-brane physics

Abstract

Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physics complementary to that of recent work of Douglas.