On the boundary coupling of topological Landau-Ginzburg models

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.

D-branes from matrix factorizations

“…In particular, I want to show how matrix factorizations of W can lead to (old and new) insights about the spacetime superpotential W, and more generally, about the local and global structure of moduli spaces of D-branes in Calabi-Yau compactifications. Other recent work on the subject includes [10,11,12,13,14,15,16].…”

Defects and boundary RG flows in ℂ / ℤ d $$ \mathbb{C}/{\mathbb{Z}}_d $$

“…A more general form for the boundary coupling of Btype topological Landau-Ginzburg models is discussed in [19] but we do not use it here. The modified Landau-Ginzburg action in the topological twisted case is invariant under infinitesimal B-type supersymmetry variations iff J i E i = W as functions of X ∂ .…”

“…Then a new boundary condition is obtained from their fusion, denoted 19) by taking y → 0. The resulting boundary is then given by the tensor product of matrix factorizations Q ′ = P ⊗ Q with…”

Landau-Ginzburg to Calabi-Yau dictionary for D-branes

“…Clearly objects in P ≥i are the objects in D(gr-A ≥i ) which have a finite length free resolution. The subcategories D i and T i are then defined from the decompositions (14).…”