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arXiv 2005.03203hep-thcond-mat.str-el
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U(1)自旋Chern-Simons理论与二维Arf不变量

U(1) spin Chern-Simons theory and Arf invariants in two dimensions

Takuya Okuda, Koichi Saito, Shuichi Yokoyama

摘要:

k阶U(1)Chern-Simons理论是k阶奇数的自旋拓扑量子场论。它的动力学是由具有一定半径的紧凑玻色子的2d CFT捕获的。最近,人们认识到,可以通过使用所谓的Arf不变量对其进行修改来给CFT提供对2D自旋结构的依赖性。我们证明,可以重新组织的环面配分函数的修改CFT到一个有限的总和涉及有限数量的共形块。这使我们能够再现自旋理论的模矩阵。我们利用模矩阵计算了自旋Chern-Simons理论在透镜空间$L(a,\pm 1)$上的配分函数,并证明了对3d自旋结构的预期依赖性.

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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