Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew

TL;DR

This paper investigates the phase diagram and anomaly structures of 4D QCD matter using cobordism theory, analyzing various phases and symmetries, including topological and anomaly constraints, across different topologies and spacetime dimensions.

Contribution

It introduces a higher anomaly involving discrete symmetries in QCD phases and explores their matching using cobordism, extending the understanding of anomalies in QCD-like theories.

Findings

Identification of a higher anomaly involving discrete symmetries in QCD phases

Analysis of symmetry constraints on QCD phases on unorientable spacetimes

Discussion of anomalies and topological terms in various spacetime dimensions

Abstract

We explore QCD$_4$ quark matter, the $\mu$-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.