[数学] 上同调规范理论、颤振矩阵模型与Donaldson-Thomas 理论 [推广有奖]

摘要翻译：
研究了Calabi-Yau三元的Donaldson-Thomas理论与六维拓扑Yang-Mills理论之间的关系。我们的主要例子是平面空间上的拓扑U(N)规范理论在其库仑分支中。为了计算它的配分函数，我们对它的非对易变形采用等变局部化技术。因此，规范理论局限于非对易瞬态，而非对易瞬态可以用n色三维Young图来分类。利用ADHM形式的高维推广，我们用射影空间上某些稳定的框架相干束对这些非交换瞬态进行了几何描述。从这个形式出发，我们构造了一个拓扑矩阵量子力学，它计算了BPS态的指数，并为六维规范理论提供了一种替代方法。
---
英文标题：
《Cohomological gauge theory, quiver matrix models and Donaldson-Thomas
  theory》
---
作者：
Michele Cirafici, Annamaria Sinkovics and Richard J. Szabo
---
最新提交年份：
2008
---
分类信息：

一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
--
一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
---
PDF链接：
https://arxiv.org/pdf/0803.4188