迈向具有传播挠率的微扰单模庞加莱规范理论
Towards Perturbative Unimodular Poincaré Gauge Theories with Propagating Torsion
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中文总结 AI 辅助
该研究探讨具有传播挠率的庞加莱引力规范理论与其单模对应理论的单圈关系，发现特定背景下单模约束不改变局域单圈挠率动力学，并指出等价性的局限及扩展方向。
中文摘要 AI 辅助
我们研究了具有传播挠率的庞加莱引力规范理论的有效场论扩展与其单模对应理论之间的单圈关系。在爱因斯坦表象中，我们考虑了两个代表性的二次挠率子 sector，即完全反对称（轴向）挠率和钩反对称挠率的矢量分量。在具有零背景挠率的最大对称度规背景下，微分同胚不变且真正的单模理论在两个 sector 中产生相同的单圈行列式，重现相同的局域对数发散。我们进一步考察了具有均匀轴向或矢量挠率的平直背景，其中存在度规-挠率混合。在每种情况下，单模规范中的依赖于挠率的单圈有效作用量与真正单模表述中的该作用量由相同的物理行列式控制。因此，对于所考虑的作用量和背景，单模约束不会改变局域单圈挠率动力学。我们还阐述了这种等价性的局限性，以及一般含挠率弯曲背景所需的扩展。
英文摘要
We study the one-loop relation between an effective-field-theory extension of Poincaré gauge theories of gravity with propagating torsion and its unimodular counterpart. In the Einstein representation, we consider two representative quadratic torsion subsectors, namely totally antisymmetric (axial) torsion and the vector component of hook-antisymmetric torsion. On maximally symmetric metric backgrounds with vanishing background torsion, the diffeomorphism-invariant and genuine unimodular theories yield identical one-loop determinants in both sectors, reproducing the same local logarithmic divergences. We further examine flat backgrounds with homogeneous axial or vector torsion, where metric-torsion mixing is present. In each case, the torsion-dependent one-loop effective action in unimodular gauge and in the genuine unimodular formulation is controlled by the same physical determinant. Thus, for the actions and backgrounds considered, the unimodular constraint does not modify local one-loop torsion dynamics. We also delineate the limitations of this equivalence and the extensions needed for generic torsionful curved backgrounds.
