论文标题
U（1）旋转Chern-Simons理论和ARF不变性
U(1) spin Chern-Simons theory and Arf invariants in two dimensions
论文作者
论文摘要
级别的k u（1）Chern-Simons理论是k奇数的自旋拓扑量子场理论。它的动力学是通过具有一定半径的紧凑型玻色子的2D CFT捕获的。最近，人们认识到，可以使用所谓的ARF不变性对CFT进行对2D旋转结构的依赖性。我们证明，可以将修改后的CFT的圆环分区函数重组为有限数量的共形块。这使我们能够重现自旋理论的模块化矩阵。我们使用模块化矩阵来计算镜头空间$ l（a，\ pm 1）$的旋转Chern-Simons理论的分区函数，并演示了对3D旋转结构的预期依赖性。
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin structure can be given to the CFT by modifying it using the so-called Arf invariant. We demonstrate that one can reorganize the torus partition function of the modified CFT into a finite sum involving a finite number of conformal blocks. This allows us to reproduce the modular matrices of the spin theory. We use the modular matrices to calculate the partition function of the spin Chern-Simons theory on the lens space $L(a,\pm 1)$, and demonstrate the expected dependence on the 3d spin structure.
