We study global anomalies of nonlocal effective theories proposed to describe symmetry-preserving Luttinger surfaces, i.e., the momentum-space manifolds of Green's function zeros (GFZs) at zero energy, in strongly interacting fermionic systems. In particular, we focus on simplest possible cases associated with a gapless Dirac zero, which is the counterpart of the gapless Dirac quasiparticle in weakly interacting systems. These theories may be derived by integrating out low-energy degrees of freedom that do not couple to the relevant gauge field. We discuss the global anomaly, the bulk-boundary correspondence, and the constraint on phases consistent with the anomaly, such as non-Fermi liquids and emergent gapless quasiparticles on Luttinger surfaces. Failing to avoid a spontaneous symmetry breaking in the thermodynamical limit inevitably leads unstable GFZs. We also provide some perspectives on why the related nonlocal fermionic effective theory studied recently is not a suitable starting point for a symmetrically gapped phase.
Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
利用带有Wess-Zumino项的非线性西格玛模型（NLSM）描述整数量子Hall（BIQH）和拓扑绝缘体（BTI）相的边界，研究了这两种相的玻色子类似物边界的微扰和全局反常.本文的主要结果之一是，这些异常是强大的对任意平滑变形的目标空间的NLSM描述的相位，只要变形也尊重相位的对称性。本文第一部分讨论了奇维时空中BIQH态边界的微扰$U(1)$反常。第二部分研究了偶维BTI态边界的整体反常。在以前的工作中[Phys. Rev. B 95，035149（2017）]，我们认为BTI相的边界表现出全局异常，这是三维狄拉克费米子奇偶异常的模拟。在这里，我们提升这个参数的二维BTI状态的边界的证明，明确计算的配分函数的规范NLSM描述的边界。然后，我们使用功能强大的等变定位技术表明，这种全球性的异常是强大的对所有的NLSM的目标空间的光滑变形，保持$U(1)\rtimes\mathbb{Z}_2$对称性的BTI状态。我们还评论的困难，后者的推广证明更高的维度。最后，我们讨论了当耦合常数在重整化群下流动时，本文所研究的边界理论的预期低能行为。
