D-brane effective action and tachyon condensation in topological minimal models

TL;DR

This paper investigates D-brane moduli spaces and tachyon condensation in topological minimal models, proposing a formula for the effective potential and analyzing examples to connect algebraic geometry with string theory.

Contribution

It introduces a closed formula for the effective deformation potential in topological minimal models and links it to categorical and matrix model descriptions.

Findings

Moduli space stratification according to brane decompositions

Derived a formula for the effective deformation potential

Provided a complete algebraic description of specific moduli spaces

Abstract

We study D-brane moduli spaces and tachyon condensation in B-type topological minimal models and their massive deformations. We show that any B-type brane is isomorphic with a direct sum of `minimal' branes, and that its moduli space is stratified according to the type of such decompositions. Using the Landau-Ginzburg formulation, we propose a closed formula for the effective deformation potential, defined as the generating function of tree-level open string amplitudes in the presence of D-branes. This provides a direct link to the categorical description, and can be formulated in terms of holomorphic matrix models. We also check that the critical locus of this potential reproduces the D-branes' moduli space as expected from general considerations. Using these tools, we perform a detailed analysis of a few examples, for which we obtain a complete algebro-geometric description of moduli spaces and strata.