Stability of Landau-Ginzburg branes

Details Stability of Landau-Ginzburg branes Stability of Landau-Ginzburg branes

2004-12-22

arxiv.org/abs/hep-th/0412274v4

J.Math.Phys. 46 (2005) 082305

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, LaTeX, summary added

Scientific paper

10.1063/1.2007590

We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli space of compact Calabi-Yau manifolds, using matrix factorizations to B-model the topological D-brane category. The standard requirement of unitarity at the IR fixed point is argued to lead to a notion of "R-stability" for matrix factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic at the Landau-Ginzburg point is not obviously unstable. Aiming to relate R-stability to a moduli space problem, we then study the action of the gauge group of similarity transformations on matrix factorizations. We define a naive moment map-like flow on the gauge orbits and use it to study boundary flows in several examples. Gauge transformations of non-zero degree play an interesting role for brane-antibrane annihilation. We also give a careful exposition of the grading of the Landau-Ginzburg category of B-branes, and prove an index theorem for matrix factorizations.

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