2+ 1维非阿贝尔规范场对偶的格构
Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
摘要：
欧氏路径积分的格构是导出U $(1)$规范场2+ 1维场论对偶的一种成功方法。在这项工作中，我们将这种格结构推广到具有非阿贝尔规范场的对偶。我们构造了具有强相互作用的$SO(3)$矢量玻色子和Majorana费米子耦合到$SO(3)$规范场的理论的欧几里德时空格点路径积分，并导出了该理论与时空格点上的自由Majorana费米子理论之间的精确对偶性.我们认为，这种晶格的对偶性意味着所需的红外线之间的耦合到$SO(3)_1$陈-西蒙斯规范理论，和一个自由的无质量的马约拉纳费米子在2+1D的场论与$SO(3)$矢量临界玻色子的对偶性。我们还将对偶的格构推广到具有$O(3)$规范场的模型。
英文摘要：
The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a U$(1)$ gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean spacetime lattice path integral for a theory with strongly-interacting $SO(3)$ vector bosons and Majorana fermions coupled to an $SO(3)$ gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the spacetime lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an $SO(3)$ vector critical boson coupled to an $SO(3)_1$ Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with $O(3)$ gauge fields.
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