F-term equations near Gepner points

TL;DR

This work develops a precise, algebraic framework for D-brane moduli in Landau-Ginzburg orbifolds via matrix factorizations, enabling exact computation of F-term constraints and brane superpotentials. By analyzing cases with $\hat{c}=1$ (torus) and $\hat{c}=3$ (quintic), it demonstrates that brane deformations can be unobstructed, obstructed, or able to lift bulk moduli, and reveals a nontrivial global structure of the BRST operator on brane moduli. The torus example shows the brane moduli space is itself a torus and that $Q$ is a nontrivial section of a bundle over moduli, while the quintic study connects F-term constraints to mirror geometry and RP$^3$ brane pairs, highlighting global line-bundle data and real-geometry interpretations. The paper also extends these ideas to other models, illustrating bulk-brane obstruction phenomena at higher order and noncommuting boundary deformations, thereby offering a concrete, computable handle on 4d $\mathcal{N}=1$ superpotentials in compact Calabi–Yau settings.

Abstract

We study marginal deformations of B-type D-branes in Landau-Ginzburg orbifolds. The general setup of matrix factorizations allows for exact computations of F-term equations in the low-energy effective theory which are much simpler than in a corresponding geometric description. We present a number of obstructed and unobstructed examples in detail, including one in which a closed string modulus is obstructed by the presence of D-branes. In a certain example, we find a non-trivial global structure of the BRST operator on the moduli space of branes.