Worldsheet approaches to D-branes on supersymmetric cycles

TL;DR

This work investigates D-branes wrapped on supersymmetric cycles in Calabi-Yau spaces using two complementary worldsheet frameworks: Landau-Ginzburg models with boundary and boundary states in Gepner models. By exploiting spectral-flow invariant constructions and discrete symmetries, it relates LG boundary conditions to Gepner boundary states and extends the bulk CY-LG correspondence to D-brane sectors. The authors provide explicit analyses for simple Gepner models (1^3, 2^2) and discuss their geometric interpretations (real and special Lagrangian cycles) alongside more complex cases (1^6), highlighting the method's generality and its potential extension to K3 and CY3 compactifications. They also discuss S-matrix resolution, boundary-state normalization, and prospects for index calculations and linear sigma-model approaches with boundaries as avenues for further work.

Abstract

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N=2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using the common discrete symmetries of the two descriptions. We are thus able to provide an extension to the boundary of the bulk correspondence between Landau-Ginzburg orbifolds and the corresponding Gepner models.