KEK 素粒子原子核研究所 理論セミナー ( 奥田 拓也 氏 )
|講演者||Dr. 奥田 拓也 ( 東京大学 )|
The level-k U(1) Chern-Simons theory with k odd is an example of spin topological quantum field theory (spin TQFT), i.e., a TQFT whose partition functions and states depend on the spin structure of spacetime. Its dynamics is expected to be captured by the 2d CFT of a free compact boson with a certain radius. Recently it was recognized that an appropriate dependence on the 2d spin structure can be given to the CFT by modifying the theory using the so-called Arf invariant. We demonstrate that one can reorganize the torus partition function of the modified CFT into a 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, and demonstrate the expected dependence on the 3d spin structure. As an introduction to the topic the talk will include an elementary review of the topological phase of matter.