Obstructions and lines of marginal stability from the world-sheet

TL;DR

This paper investigates how supersymmetric D-branes behave under background deformations using world-sheet methods, explaining the origin of lines of marginal stability and obstructions, with distinctions between N=2 and N=4 superconformal cases.

Contribution

It provides a detailed world-sheet analysis of obstructions and lines of marginal stability for supersymmetric D-branes, highlighting differences between N=2 and N=4 superconformal theories.

Findings

N=2 B-type branes can be obstructed by (cc) perturbations.

Obstructions do not occur for N=4 superconformal branes at c=6.

The analysis combines superspace field theory and perturbed conformal field theory techniques.

Abstract

The behaviour of supersymmetric D-branes under deformations of the closed string background is studied using world-sheet methods. We explain how lines of marginal stability and obstructions arise from this point of view. We also show why N=2 B-type branes may be obstructed against (cc) perturbations, but why such obstructions do not occur for N=4 superconformal branes at c=6, i.e. for half-supersymmetric D-branes on K3. Our analysis is based on a field theory approach in superspace, as well as on techniques from perturbed conformal field theory.