D-brane superpotentials and RG flows on the quintic

TL;DR

The work addresses how D2-branes on the quintic Calabi–Yau react to complex structure deformations, showing that bulk-induced boundary RG flows are gradient flows of an effective spacetime superpotential. By merging Landau–Ginzburg matrix factorisations with topological CFT data, it computes bulk–boundary couplings exactly (to all orders in boundary data and to first order in bulk perturbations) and derives an explicit open–closed superpotential controlled by an Abel–Jacobi-type integral on the brane moduli space. The results reveal that generic complex structure deformations lift the continuous brane moduli to a finite set of fixed points (10 in the studied family), with the RG flow guiding branes along the moduli to these minima. Connections are made to holomorphic Chern–Simons theory, Picard–Fuchs-type structures for open strings, and mirror-symmetry interpretations involving disc instantons, offering a framework that extends to broader Calabi–Yau settings and brane configurations.

Abstract

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.