三种壁穿越公式的等价性
高能物理 - 理论
2012-12-06 v3 代数几何
摘要
Kontsevich 和 Soibelman 的壁穿越公式通过将由壁两侧 BPS 指标构造的两个辛同胚相等，给出了临界稳定性壁两侧 BPS 指标之间的隐式关系。Manschot、Pioline 与本文作者提出的壁穿越公式则给出了用另一侧 BPS 指标表示的、壁一侧 BPS 指标的两个看似不同的显式表达式。我们证明了这三种公式的等价性。
引用
@article{arxiv.1112.2515,
title = {Equivalence of Three Wall Crossing Formulae},
author = {Ashoke Sen},
journal= {arXiv preprint arXiv:1112.2515},
year = {2012}
}
备注
LaTeX file, 45 pages; v2: added eq.(2.10) containing explicit wall crossing formula for numerical invariants and comments on its possible connection to Joyce-Song formula, added references and some additional minor clarifications; added a simpler proof suggested by the anonymous referee, added other clarifications, version to appear in CNTP, 51 pages