We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface together with a defect network dual to the triangulation. Independence of the triangulation and of the other choices follows if the line defect and junctions are obtained from a Delta-separable Frobenius algebra with involutive Nakayama automorphism in the monoidal category of topological defects. For rational conformal field theory we can give a more explicit description of the defect category, and we work out two examples related to free fermions in detail: the Ising model and the so(n) WZW model at level 1.

中文翻译：

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从二维量子场论中的缺陷自旋

我们从具有拓扑缺陷线和结网络的定向表面的理论开始，在自旋表面上建立二维量子场论。该构造根据配备额外数据的三角剖分使用自旋结构的组合描述。自旋表面的振幅被定义为下层定向表面的振幅以及对三角测量的双重缺陷网络。如果线缺陷和连接点是从具有拓扑缺陷的幺半群类别中的对合 Nakayama 自同构的 Delta 可分 Frobenius 代数获得的，则三角剖分和其他选择的独立性随之而来。对于有理共形场论，我们可以对缺陷类别进行更明确的描述，并详细计算出两个与自由费米子相关的例子：