8维ADHM、着色立体分拆与轨形上的Donaldson-Thomas不变量
ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
AI总结：
本研究用类ADHM箭图构造研究非交换${\mathbb C}^4$上超对称规范理论的$SU(4)$不变BPS模空间，以立体分拆分类解，轨形情形用着色立体分拆，还算出相关配分函数，猜想其对应轨形Donaldson-Thomas不变量。
摘要：
我们借助类ADHM箭图构造，研究非交换${\mathbb C}^4$上超对称规范理论中$SU(4)$不变BPS条件的模空间，并依据自然环面作用，以立体分拆对不变解进行分类。在轨形${\mathbb C}^4/G$（$G$为$SU(4)$的有限子群）情形下，分类以着色立体分拆给出。其计数的统计权重通过关联的等变上同调规范理论定义。我们显式计算了它在${\mathbb C}^4$和${\mathbb C}^2\times\left({\mathbb C}^2/{\mathbb Z}_2\right)$上的配分函数，该函数据猜想给出了对应的轨形Donaldson-Thomas不变量。
英文摘要：
We study the moduli space of $SU(4)$ invariant BPS conditions in supersymmetric gauge theory on non-commutative ${\mathbb C}^4$ by means of an ADHM-like quiver construction and we classify the invariant solutions under the natural toric action in terms of solid partitions. In the orbifold case ${\mathbb C}^4/G$, $G$ being a finite subgroup of $SU(4)$, the classification is given in terms of coloured solid partitions. The statistical weight for their counting is defined through the associated equivariant cohomological gauge theory. We explicitly compute its partition function on ${\mathbb C}^4$ and ${\mathbb C}^2\times\left({\mathbb C}^2/{\mathbb Z}_2\right)$ which conjecturally provides the corresponding orbifold Donaldson-Thomas invariants.
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