论文标题
超符合量子力学和捆捆同学的增长
Superconformal Quantum Mechanics and Growth of Sheaf Cohomology
论文作者
论文摘要
我们给出了在具有模化符号分辨率的超级量子锥上定义的超符号量子力学的几何解释。 BPS状态在已解决的空间上具有某些扭曲的Dolbeault协同学类别，其索引归化性也可能与在e夫式的分层协同学中计算的欧拉特征有关。在C2上K点的Hilbert方案的特殊情况下，我们获得了BPS状态指数变性的指数增长的严格估计值，因为K到达了无穷大。这种增长是我们最近提出的七维黑洞和超符合量子力学之间二元性的玩具模型。
We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kahler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the resolved space and their index degeneracies can also be related to the Euler characteristic computed in equivariant sheaf cohomology. In the special case of the Hilbert scheme of K points on C2, we obtain a rigorous estimate for the exponential growth of the index degeneracies of BPS states as K goes to infinity. This growth serves as a toy model for our recently proposed duality between a seven dimensional black hole and superconformal quantum mechanics.
