Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT
Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT
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发表时间：
2022
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通讯作者：
Shih-Hsuan Chen
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作者：
Shih-Hsuan Chen
孤子对称被认为遵循拓扑孤子的同伦群分类。在这里，我们指出了一个更复杂的代数结构，当不同维度的孤子共存于谱。我们在一个具体的量子场论中揭示了这一现象，即4d cp1模型。该模型有两种孤子激励，旋涡和希望，它们按照同伦群遵循两个U(1)孤子对称。然而，我们通过计算涡旋算子的hopon电荷证明了hopon U(1)对称性的不存在性。我们阐明了由三维自旋拓扑量子场论（tqft）产生的不可逆对称性是守恒hopon数的。它的可逆部分是z2，我们认为它是自旋体不变量。与三维cp1模型相比，我们的工作提出了对孤子对称性和拓扑相耦合的统一描述。
Solitonic symmetry is believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover this phenomenon in a concrete quantum field theory, the 4d C P 1 model. This model has two kinds of solitonic excitations, vortices and hopfions, which would follow two U (1) solitonic symmetries according to homotopy groups. Nevertheless, we demonstrate the nonexistence of the hopfion U (1) symmetry by evaluating the hopfion charge of vortex operators. We clarify that what conserves hopfion numbers is a non-invertible symmetry generated by 3d spin topological quantum field theories (TQFTs). Its invertible part is just Z 2 , which we recognize as a spin bordism invariant. Compared with the 3d C P 1 model, our work suggests a unified description of solitonic symmetries and couplings to topological phases.