On Superpotentials for D-Branes in Gepner Models

TL;DR

This paper develops methods to compute open string amplitudes for D-branes in Gepner models, providing explicit formulas and analyzing boundary theories related to special Lagrangian submanifolds in Calabi-Yau spaces.

Contribution

It introduces new computational techniques for open string amplitudes in Gepner model D-branes, including explicit vertex operator product formulas.

Findings

Explicit formulas for open string vertex operator products.

Boundary theories of the quintic have no continuous moduli.

Methods applicable to a large class of D-branes in Calabi-Yau spaces.

Abstract

A large class of D-branes in Calabi-Yau spaces can be constructed at the Gepner points using the techniques of boundary conformal field theory. In this note we develop methods that allow to compute open string amplitudes for such D-branes. In particular, we present explicit formulas for the products of open string vertex operators of untwisted A-type branes. As an application we show that the boundary theories of the quintic associated with the special Lagrangian submanifolds Im \omega_i z_i = 0 where \omega_i^5=1 possess no continuous moduli.