We explore QCD₄ quark matter, the μ-T (chemical potential-temperature) phase diagram, possible 't Hooft anomalies, and topological terms, via non-perturbative tools of cobordism theory and higher anomaly matching. We focus on quarks in 3-color and 3-flavor on bi-fundamentals of SU(3), then analyze the continuous and discrete global symmetries and pay careful attention to finite group sectors. We input constraints from $T=CP$ or CT time-reversal symmetries, implementing QCD on unorientable spacetimes and distinct topology. Examined phases include the high T QGP (quark-gluon plasma/liquid), the low T ChSB (chiral symmetry breaking), 2SC (2-color superconductivity) and CFL (3-color-flavor locking superconductivity) at high density. We introduce a possibly useful but only approximate higher anomaly, involving discrete 0-form axial and 1-form mixed chiral-flavor-locked center symmetries, matched by the above four QCD phases. We also enlist as much as possible, but without identifying all of, 't Hooft anomalies and topological terms relevant to Symmetry Protected/Enriched Topological states (SPTs/SETs) of gauged SU(2) or SU(3) QCD_d-like matter theories in general in any spacetime dimensions $d=2,3,4,5$ via cobordism.

我们通过Cobordism理论的非扰动工具和较高的异常匹配来探索QCD ₄夸克物质，μ -T（化学势-温度）相图，可能的't Hooft异常和拓扑项。我们着重于SU（3）的三基色的夸克的3色和3味的夸克，然后分析连续和离散的全局对称性，并注意有限的组扇区。我们输入约束$Ť=CP$或CT时间反转对称性，在无法定向的时空和独特的拓扑结构上实施QCD。检查阶段包括高密度的高T QGP（夸克胶子血浆/液体），低T ChSB（手性对称断裂），2SC（2色超导）和CFL（3色锁定超导）。我们介绍了一个可能有用但仅近似的较高异常，涉及离散的0形轴向和1形混合手性风味锁定中心对称，与上述四个QCD相匹配。我们还尽可能多地征募，但没有找到所有与规范SU（2）或SU（3）QCD _d的对称保护/丰富拓扑状态（SPTs / SET）相关的Hooft异常和拓扑术语。时空维度的类物质理论 $d=2，3，4，5$ 通过合作主义。