On the boundary coupling of topological Landau-Ginzburg models

TL;DR

The paper develops a generalized boundary coupling for B-type topological Landau-Ginzburg models with noncompact Calabi-Yau targets by promoting the open-string background to a $(0,1)$ superconnection on a complex superbundle $E$. Building on Witten's approach to boundary actions, it uses a twisted formulation to derive BRST invariance conditions, showing that the BRST variation enforces the $(0,\leq 2)$-part of the superconnection curvature to satisfy ${\cal F}^{(0,\leq 2)} = c + W\,\mathrm{id}_E$, where $W$ is the LG potential and $c$ a constant endomorphism. This result extends the known BRST/open-string equations from the Abelian to the non-Abelian setting and situates B-type LG branes as tachyon-condensed composites of elementary B-model branes. In the $W=0$ limit, the framework recovers the conventional ${\cal F}^{(0,\leq 2)}=0$ condition, linking open LG dynamics to the established B-model boundary data while clarifying how boundary degrees of freedom encode nontrivial open-string dynamics. The work provides a coherent target-space perspective on open LG branes and their equations of motion, illustrating how boundary holonomies capture BRST-consistent boundary deformations.

Abstract

I propose a general form for the boundary coupling of B-type topological Landau-Ginzburg models. In particular, I show that the relevant background in the open string sector is a (generally non-Abelian) superconnection of type (0,1) living in a complex superbundle defined on the target space, which I allow to be a non-compact Calabi-Yau manifold. This extends and clarifies previous proposals. Generalizing an argument due to Witten, I show that BRST invariance of the partition function on the worldsheet amounts to the condition that the (0,<= 2) part of the superconnection's curvature equals a constant endomorphism plus the Landau-Ginzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model.