Obstructed D-Branes in Landau-Ginzburg Orbifolds
Sujay K. Ashok, Eleonora Dell'Aquila, Duiliu-Emanuel Diaconescu,, Bogdan Florea
TL;DR
This paper investigates the deformation theory of Landau-Ginzburg D-branes associated with obstructed rational curves on Calabi-Yau threefolds, using homotopy algebra to determine moduli spaces and superpotentials, exemplified on lines on a perturbed Fermat quintic.
Contribution
It provides a detailed computation of D-brane moduli spaces and superpotentials in Landau-Ginzburg orbifolds, connecting algebraic structures to geometric curve deformations.
Findings
Reproduces the local structure of the Hilbert scheme of curves.
Calculates D-brane superpotentials via higher products in the orbifold category.
Analyzes obstructed rational curves on Calabi-Yau threefolds.
Abstract
We study deformations of Landau-Ginzburg D-branes corresponding to obstructed rational curves on Calabi-Yau threefolds. We determine D-brane moduli spaces and D-brane superpotentials by evaluating higher products up to homotopy in the Landau-Ginzburg orbifold category. For concreteness we work out the details for lines on a perturbed Fermat quintic. In this case we show that our results reproduce the local analytic structure of the Hilbert scheme of curves on the threefold.
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