论文标题
较高的浆果阶段和索引定理
Higher Berry Phase of Fermions and Index Theorem
论文作者
论文摘要
当量子场理论被微不足道时，其红外固定点是可逆场理论。可逆字段理论的分区函数在长距离限制中记录了对各种背景字段的响应。背景字段的集合可以包括时空依赖性耦合常数，在这种情况下，我们将相应的可逆理论称为参数化的可逆场理论。我们研究了使用Atiyah-Patodi-Singer索引定理用于超级连接定理，该参数化的可逆场理论与时空依赖性质量参数产生。特别是，对质量的无限调制的响应被编码为浆果曲率的较高类似物，为此我们提供了一般的公式。当浆果曲率消失时，如果存在剩余的扭转浆阶段，那么可逆理论仍然可能是不乏味的，我们列出了一些可计算的示例。
When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background fields in the long-distance limit. The set of background fields can include spacetime-dependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory. We study such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters using the Atiyah-Patodi-Singer index theorem for superconnections. In particular, the response to an infinitesimal modulation of the mass is encoded into a higher analog of the Berry curvature, for which we provide a general formula. When the Berry curvature vanishes, the invertible theory can still be nontrivial if there is a remaining torsional Berry phase, for which we list some computable examples.
