标题： 挠率存在时的外尔上同调与共形反常 显示英文标题

标题： Weyl cohomology and the conformal anomaly in the presence of torsion

摘要： 利用上同调方法，我们在存在矢量型挠率的 $d=2,4$ 维情形下，识别了共形反常中的平凡和非平凡贡献。 在这两种情况下，我们的分析考虑了两种情景：一种是挠率矢量以仿射方式变换，即它是 Weyl 变换的规范势；另一种是它在 Weyl 群下不变。 对于前者，在 $d=2,4$ 中的一个重要结果是，关于 Deser 和 Schwimmer 的分类，出现了“混合”性质的反常。 对于 $d=4$ 中的不变挠率，我们还发现了一种新的反常，我们称之为 $\Psi$-反常。 考虑到这些结果，我们将不同的反常整合起来得到重整化的反常有效作用量。 之后，我们将这些作用量改写为协变的非局域形式和局域形式，后者更易于处理。 在此过程中，我们停下来讨论这些有效作用量的物理实用性，特别是用于获得 $2d$ 黑洞的重整化能动张量和热力学。 显示英文摘要

摘要： Using cohomological methods, we identify both trivial and nontrivial contributions to the conformal anomaly in the presence of vectorial torsion in $d=2,4$ dimensions. In both cases, our analysis considers two scenarios: one in which the torsion vector transforms in an affine way, i.e., it is a gauge potential for Weyl transformations, and the other in which it is invariant under the Weyl group. An important outcome for the former case in both $d=2,4$ is the presence of anomalies of a "mixed" nature in relation to the classification of Deser and Schwimmer. For invariant torsion in $d=4$, we also find a new type of anomaly which we dub $\Psi$-anomaly. Taking these results into account, we integrate the different anomalies to obtain renormalized anomalous effective actions. Thereafter, we recast such actions in the covariant nonlocal and local forms, the latter being easier to work with. Along the way, we pause to comment on the physical usefulness of these effective actions, in particular to obtain renormalized energy-momentum tensors and thermodynamics of $2d$ black holes.