Communications in Mathematical Physics Wall-Crossing , Free Fermions and Crystal Melting
Communications in Mathematical Physics Wall-Crossing , Free Fermions and Crystal Melting
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发表时间：
2010
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通讯作者：
P. Sułkowski
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作者：
P. Sułkowski
我们从自由费米子、顶点算子和晶体熔化的角度描述了局部的、没有紧化四环的环状Calabi-Yau流形的壁交叉。首先，我们将自由费米子希尔伯特空间中的两个态与每个这样的流形联系起来。这些态的重叠再现了由拓扑弦配分函数的模平方给出的非交换Donaldson-Thomas不变量对应的BPS配分函数。其次，我们引入了表示与流形中每两个循环的b场变化相关的边缘稳定性的跨壁算子。非平凡腔室中的BPS配分函数由这些算子的期望值给出。第三，我们讨论了这类流形的相关器的晶体解释。我们描述了这些晶体在模量变化时的演化，并找到了翻牌转变和DT/PT转变的晶体解释。我们发现的晶体对近年来文献中出现的各种卡拉比-丘晶体模型进行了推广和统一。
We describe wall-crossing for local, toric Calabi-Yau manifolds without compact four-cycles, in terms of free fermions, vertex operators, and crystal melting. Firstly, to each such manifold we associate two states in the free fermion Hilbert space. The overlap of these states reproduces the BPS partition function corresponding to the noncommutative Donaldson-Thomas invariants, given by the modulus square of the topological string partition function. Secondly, we introduce the wall-crossing operators which represent crossing the walls of marginal stability associated to changes of the B-field through each two-cycle in the manifold. BPS partition functions in non-trivial chambers are given by the expectation values of these operators. Thirdly, we discuss crystal interpretation of such correlators for this whole class of manifolds. We describe evolution of these crystals upon a change of the moduli, and find crystal interpretation of the flop transition and the DT/PT transition. The crystals which we find generalize and unify various other Calabi-Yau crystal models which appeared in literature in recent years.