Refined, Motivic, and Quantum
Refined, Motivic, and Quantum
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DOI：
10.1007/s11005-009-0357-9
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发表时间：
2009-04
影响因子：
1.2
通讯作者：
Tudor Dimofte;S. Gukov
中科院分区：
文献类型：
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作者：
Tudor Dimofte;S. Gukov
众所周知，在Toric Calabi-Yau流形上的弦紧化中，人们可以引入精化的BPS不变量，这些不变量不仅携带关于BPS态的电荷的信息，还携带关于自旋含量的信息。在本文中，我们研究了这些不变量在跨越墙的情况下的行为。特别地，通过应用精化的壁交叉公式，我们得到了锥形在不同腔室中的精化BPS简并度。这一结果可以用一种新的统计模型来解释，该模型计算了精化金字塔划分；该模型提供了跨墙的组合实现，并阐明了精化金字塔划分与精化拓扑点之间的关系。我们还比较了改进的BPS不变量和Kontsevich-Soibelman提出的Motivic Donaldson-Thomas不变量的穿墙行为。特别是，我们认为，在BPS状态计数的上下文中，本文标题中的三个形容词本质上是同义的。
It is well known that in string compactifications on toric Calabi–Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we study how these invariants behave under wall crossing. In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers. The result can be interpreted in terms of a new statistical model that counts “refined” pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson–Thomas invariants introduced by Kontsevich–Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.