Stability of Landau-Ginzburg branes
Abstract: We evaluate the ideas of Π-stability at the Landau-Ginzburg (LG) 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-s...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
22 August 2005
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| In: |
Journal of mathematical physics
Year: 2005, Jahrgang: 46, Heft: 8 |
| ISSN: | 1089-7658 |
| DOI: | 10.1063/1.2007590 |
| Online-Zugang: | Verlag, Volltext: https://doi.org/10.1063/1.2007590 Verlag: https://aip.scitation.org/doi/10.1063/1.2007590 
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| Verfasserangaben: | Johannes Walcher |
MARC
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| 520 | |a Abstract: We evaluate the ideas of Π-stability at the Landau-Ginzburg (LG) 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 quasihomogeneous 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 maplike flow on the gauge orbits and use it to study boundary flows in several examples. Gauge transformations of nonzero 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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