F-term equations near Gepner points

TL;DR

This paper investigates the F-term equations for B-type D-branes in Landau-Ginzburg orbifolds, revealing exact computational methods and complex moduli space structures near Gepner points.

Contribution

It provides explicit examples of obstructed and unobstructed deformations using matrix factorizations, highlighting novel global structures in the brane moduli space.

Findings

Exact F-term equations can be computed using matrix factorizations.

Identification of obstructed and unobstructed brane deformations.

Discovery of non-trivial global structure of the BRST operator on moduli space.

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.