发表机构
University of Pennsylvania; Massachusetts Institute of Technology（宾夕法尼亚大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过上同调悬挂映射计算更高反常与压缩SPTs，利用Eilenberg-MacLane空间模型在非域基环上自动化相关计算，为量子场论等的对称性研究提供了方法与结果。
AI 中文摘要
我们明确计算并制表了上同调运算的悬挂映射，将其应用于量子场论与格点系统中反常的维数约化及广义对称性的更高群结构。在具有离散p-形式对称性的量子系统中，可将对称缺陷限制在时空的余维-q子空间，等价于将规范场限制在厚度趋近于零的平板中，这会使子空间上产生(p-q)-形式对称性。我们确定了该过程中对称性的两个重要性质的变化：其一，计算约化对称性的反常，即原对称性的更高反常，其是更高规范化与 onsiteability（局域性）的阻碍；其二，对于以Postnikov类编码为更高群结构的两个对称性，计算其约化更高群结构，该结构可能非平凡。两种情况均由Eilenberg-MacLane空间上同调中q次迭代的上同调悬挂Ω（亦称循环函子或迁移）描述。经典结果表明，Ω在稳定范围内为同构，且会湮灭混合反常。为在非域的基环上计算Ω，我们利用了Cartan与Moore开创的Eilenberg-MacLane空间链DGAs的小模型，对其结果进行了综述与扩展，关键新增步骤是通过p进级数将模p链收缩改进为p局部整数。我们在软件包\texttt{emcm}中自动化了计算，并提供了大量结果表格。最后，为关联上同调运算的上链显式形式，我们演示了如何在该框架中计算杯积与特定的杯-i积。
英文摘要
We explicitly compute and tabulate the suspension map for cohomology operations, applying it to the dimensional reduction of anomalies and higher group structures of generalised symmetries in quantum field theories and lattice systems. In a quantum system with a discrete $p$-form symmetry, we can restrict the symmetry defects to a codimension-$q$ subspace of spacetime, or equivalently confine the gauge field to a slab whose thickness approaches zero. This results in a $(p-q)$-form symmetry on the subspace. We determine the fate of two important properties of symmetries under this process. First, we compute the anomaly of the reduced symmetry, or the higher anomaly of the original symmetry, which acts as an obstruction to higher gauging and onsiteability. Second, for two symmetries forming a higher-group structure, encoded as a Postnikov class, we compute the reduced higher-group structure, which may or may not be trivial. Both cases are captured by the $q$-fold iteration of the cohomology suspension $Ω$, also known as the loop functor or transgression, in the cohomology of Eilenberg--MacLane spaces. Classical results state that $Ω$ is an isomorphism in a stable range and annihilates mixed anomalies. To calculate $Ω$ over a base ring which is not a field, we make use of small models for the chain DGAs of Eilenberg--MacLane spaces, pioneered by Cartan and Moore, whose results we review and extend. The critical added step is the improvement of a mod $p$ chain contraction to the $p$-local integers, obtained via a $p$-adic series. We automate the computations in a software package \texttt{emcm}, and provide extensive tables of the results. Finally, to make contact with explicit cochain formulations of cohomology operations, we demonstrate how to calculate cup products and certain cup-$i$ products in this framework.
Comments40 pages + appendices, 4 figures
