Solitons in Seiberg-Witten Theory and D-branes in the Derived Category

TL;DR

This paper explores the connection between BPS solitons in N=2 SU(2) gauge theory and D-branes in the derived category, using geometric engineering and Pi-stability to explicitly reproduce known spectra.

Contribution

It demonstrates how the derived category and Pi-stability framework can explicitly reproduce BPS spectra in geometric engineering of gauge theories.

Findings

Derived category and Pi-stability reproduce BPS spectra explicitly.

Analysis reduces to derived category of CP1.

Provides a geometric engineering perspective on solitons.

Abstract

We analyze the "geometric engineering" limit of a type II string on a suitable Calabi-Yau threefold to obtain an N=2 pure SU(2) gauge theory. The derived category picture together with Pi-stability of B-branes beautifully reproduces the known spectrum of BPS solitons in this case in a very explicit way. Much of the analysis is particularly easy since it can be reduced to questions about the derived category of CP1.