Loop models, modular invariance, and three-dimensional bosonization
Loop models, modular invariance, and three-dimensional bosonization
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DOI：
10.1103/physrevb.97.195112
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发表时间：
2018-01
影响因子：
3.7
通讯作者：
Hart Goldman;E. Fradkin
中科院分区：
文献类型：
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作者：
Hart Goldman;E. Fradkin
我们考虑了纯2+1维和3+1维体系统表面上的2+1维时空中具有U$(1)$规范场介导的边际远程和统计相互作用的量子环模型族。在没有分数自旋的情况下，这些理论在粒子-涡旋对偶下是自对偶的，并且环路的统计角度移动了$2\pi$，形成了模群PSL$(2,\mathbb{Z})$的一个子群。我们表明，在这些理论中仔细考虑分数自旋完全打破了它们的统计周期性，并描述了这是如何发生的，解决了与它们在临界状态下接近的共形场理论的分歧。我们明确地证明了分数自旋的结合导致了与最近的2+1维场论对偶网络平行的环模型对偶，并提供了对其有效性的非平凡检验。
We consider a family of quantum loop models in 2+1 spacetime dimensions with marginally long-ranged and statistical interactions mediated by a U$(1)$ gauge field, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk system. In the absence of fractional spin, these theories have been shown to be self-dual under particle-vortex duality and shifts of the statistical angle of the loops by $2\pi$, which form a subgroup of the modular group, PSL$(2,\mathbb{Z})$. We show that careful consideration of fractional spin in these theories completely breaks their statistical periodicity and describe how this occurs, resolving a disagreement with the conformal field theories they appear to approach at criticality. We show explicitly that incorporation of fractional spin leads to loop model dualities which parallel the recent web of 2+1 dimensional field theory dualities, providing a nontrivial check on its validity.