Compact nonlocal Abelian gauge theory in (2 + 1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3 + 1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T 3 $$ {\mathbbm{T}}_3 $$ . Analogous results for the S 2 × S 1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

中文翻译：

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(2 + 1) 维自对偶共形理论的量化

(2 + 1) 维的紧凑非局部阿贝尔规范理论，也称为循环模型，是一种无质量理论，其临界线在对偶变换下显式协变。它对应于混合三四维中自双电动力学的大 NF 极限。它还为三维拓扑绝缘体的表面激发提供了玻色子描述。在将模型映射到 (3 + 1) 维的局部规范理论后，我们计算了电和磁孤子激发的频谱以及三个环面 T 3 $$ {\mathbbm{T}}_3 $$ 上的配分函数。S 2 × S 1 几何的类似结果表明，该理论是共形不变的，并确定了共形场的明显自对偶谱，对应于具有分数统计的有序-无序激发。