标题： 非微扰混合反常和分数流体输运 显示英文标题

标题： A Non-Perturbative Mixed Anomaly and Fractional Hydrodynamic Transport

摘要： 我们提出了一种新的非微扰的't Hooft anomaly，它影响着四维具有对称群 $G=U(1)\times \mathbb{Z}_2$ 的量子场论。 我们使用Adams谱序列计算得出，bordism群 $\Omega^\text{Spin}_5(BG)$（该群分类了当微扰异常消失后仍存在的异常）是 $\mathbb{Z}_4$。 通过构造一个映射环面并评估Atiyah-Patodi-Singer $\eta$-不变量，我们证明了模4异常是由一对在 $U(1)$下矢量式的Weyl费米子生成的，但其中只有一个分量在 $\mathbb{Z}_2$下带电。 我们在流体力学极限之前构建了一个简单的微观场理论来实现这个异常，并研究了它的影响。 我们发现，反常性支配着类似于手征涡旋效应和磁效应的输运现象$U(1)$电流和能量-动量张量（尽管这里的微扰反常消失），但电导率以四分之一为单位进行分数量化，反映了边界群的 mod 4 性质。在此过程中，我们在所有度数$d=0$到 5 中计算了相关的边界群$\Omega^\text{Spin}_d(B\mathbb{Z}_2\times BU(1))$和$\Omega_d^{\text{Pin}^-}(BU(1))$。 显示英文摘要

摘要： We present a new non-perturbative 't Hooft anomaly afflicting a quantum field theory with symmetry group $G=U(1)\times \mathbb{Z}_2$ in four dimensions. We use the Adams spectral sequence to compute that the bordism group $\Omega^\text{Spin}_5(BG)$, which classifies anomalies that remain when perturbative anomalies cancel, is $\mathbb{Z}_4$. By constructing a mapping torus and evaluating the Atiyah-Patodi-Singer $\eta$-invariant, we show that the mod 4 anomaly is generated by a pair of Weyl fermions that are vector-like under $U(1)$, but with only one component charged under $\mathbb{Z}_2$. We construct a simple microscopic field theory that realises the anomaly, before investigating its impact in the hydrodynamic limit. We find that the anomaly dictates transport phenomena in the $U(1)$ current and energy-momentum tensor akin to the chiral vortical and magnetic effects (even though the perturbative anomalies here vanish), but with the conductivities being fractionally quantised in units of a quarter, reflecting the mod 4 nature of the bordism group.Along the way, we compute the (relevant) bordism groups $\Omega^\text{Spin}_d(B\mathbb{Z}_2\times BU(1))$ and $\Omega_d^{\text{Pin}^-}(BU(1))$ in all degrees $d=0$ through 5.