论文标题
关于QFT，异常和应用程序中浆果连接的评论
Remarks on Berry Connection in QFT, Anomalies, and Applications
论文作者
论文摘要
浆果连接最近已被推广到更高维度的QFT，可以将其视为有效的背景耦合作用中的拓扑术语。通过流入，该术语对应于耦合空间中的边界异常，这是文献中最近引入的另一个概念。在本说明中，我们解决了一个问题的问题，即在$σ^{（d）} \ times \ times \ mathbb {r} $上，QFT中是否仍然有意义，其中$σ^{（d）} $是$ d $ d $ d $ -dimensional compact Space and $ \ time。 $σ^{（d）} $的紧凑性使我们减轻了IR差异，因此我们只需要解决紫外线问题。我们描述了浆果连接良好（包括$ tt^*$方程）的许多情况，而不是。我们还提到了与边界异常和边界状态的关系。然后，我们确定了免费的3D Dirac Fermion和3D $ \ Mathcal {n} = 2 $手性多重的示例。最后，我们考虑$ \ mathbb {t}^2 \ times \ mathbb {r} $上的3D理论，其中空间$ \ mathbb {t}^2 $是两螺旋，并应用我们的机械来澄清3D Susy Vacua和Elliptic Coohomology之间关系的某些方面。我们还评论了对更高属的概括。
Berry connection has been recently generalized to higher-dimensional QFT, where it can be thought of as a topological term in the effective action for background couplings. Via the inflow, this term corresponds to the boundary anomaly in the space of couplings, another notion recently introduced in the literature. In this note we address the question of whether the old-fashioned Berry connection (for time-dependent couplings) still makes sense in a QFT on $Σ^{(d)}\times \mathbb{R}$, where $Σ^{(d)}$ is a $d$-dimensional compact space and $\mathbb{R}$ is time. Compactness of $Σ^{(d)}$ relieves us of the IR divergences, so we only have to address the UV issues. We describe a number of cases when the Berry connection is well defined (which includes the $tt^*$ equations), and when it is not. We also mention a relation to the boundary anomalies and boundary states on the Euclidean $Σ^{(d)} \times \mathbb{R}_{\geq 0}$. We then work out the examples of a free 3D Dirac fermion and a 3D $\mathcal{N}=2$ chiral multiplet. Finally, we consider 3D theories on $\mathbb{T}^2\times \mathbb{R}$, where the space $\mathbb{T}^2$ is a two-torus, and apply our machinery to clarify some aspects of the relation between 3D SUSY vacua and elliptic cohomology. We also comment on the generalization to higher genus.
