论文标题
通过Chern-Simons玻色粒粒子涡旋双重性在2+1个维度中的实易
Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality
论文作者
论文摘要
二元性通过关联两个看似不同的理论来深入了解物理学。在这里，我们考虑（2+1）时空维度中的晶格费米子和玻色子之间的二元性，将自由的巨大dirac fermions与Abelian Chern-Simons Higgs（Acsh）玻色子有关。为了建立二元性，我们代表了晶格费米斯的确切分区功能，而fermionic worldines的扭曲。在玻感方面，分区函数在Acsh Lagrangian的粒子涡流偶的涡旋环的旋转中表达。在连续性和缩放限制中，我们表明它们是相同的。可以从封闭的费尔米金世界线程中理解这一结果，即Acsh涡流环的直接映射，并跟踪粒子统计数据。
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we consider a duality between lattice fermions and bosons in (2+1) spacetime dimensions, relating free massive Dirac fermions to Abelian Chern-Simons Higgs (ACSH) bosons. To establish the duality we represent the exact partition function of the lattice fermions in terms of the writhe of fermionic worldlines. On the bosonic side the partition function is expressed in the writhe of the vortex loops of the particle-vortex dual of the ACSH Lagrangian. In the continuum and scaling limit we show these to be identical. This result can be understood from the closed fermionic worldlines being direct mappings of the ACSH vortex loops, with the writhe keeping track of particle statistics.
