Triangle-generation in topological D-brane categories

TL;DR

This paper demonstrates that in topological Landau-Ginzburg models, all D-brane systems in ADE minimal models can be generated from just one or two fundamental branes, using algebraic and categorical methods.

Contribution

It provides a proof that all D-branes in ADE minimal models are generated by a small set of fundamental branes, simplifying the understanding of their structure.

Findings

All D-brane systems in ADE minimal models can be generated from one or two branes.

The approach uses commutative algebra and triangulated categories.

Explicit proofs are provided for the generation property.

Abstract

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.