On the boundary coupling of topological Landau-Ginzburg models

TL;DR

This paper introduces a comprehensive framework for boundary couplings in B-type topological Landau-Ginzburg models, describing the open string sector via superconnections on complex superbundles, and derives the conditions for BRST invariance.

Contribution

It generalizes previous models by formulating the boundary coupling as a superconnection in a non-compact Calabi-Yau setting, clarifying the target space equations of motion.

Findings

Superconnections describe boundary conditions in topological Landau-Ginzburg models.

BRST invariance leads to specific curvature conditions on the superconnection.

Framework extends to non-compact Calabi-Yau target spaces.

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.