Understanding the nature of quantum matters is one of the profound challenges of contemporary physics. Quantum field theory (QFT) serves as a powerful tool for addressing this challenge and provides the long-range effective description of many-body systems. Strongly coupled QFTs are especially interesting but also very difficult to solve.
One approach to tackle these strongly coupled field theories is to focus on global symmetries, and close look at symmetries restricts possible behaviors of dynamics. For example, the ’t Hooft anomaly represents an obstruction to promoting the global symmetry to local gauge symmetry in a quantum system. This leads to ’t Hooft anomaly matching, which requires that the global symmetry transformations remain consistent across all energy scales, putting constraints on the low-energy dynamics of QFTs. ’t Hooft anomalies thus provide important non-perturbative data for solving strongly coupled QFTs.
Global inconsistency is a recently proposed concept that serves as a milder version of the ’t Hooft anomaly. Unlike the latter, it imposes less stringent constraints by not necessarily ruling out the presence of a trivial gapped phase, and it is important to uncover its correct physical consequences.
In this study, we investigated simple quantum mechanical models with theta parameters to understand the implications of global inconsistency in comparison to ’t Hooft anomalies. Although these models are simple, they share key symmetries and also anomalies and global inconsistency with more complex QFTs.
Our results show that global inconsistency can be satisfied either by ground-state degeneracy at one of the globally inconsistent couplings or by level-crossings separating them, which leads to phase transitions between different symmetry-protected topological states in the case of quantum many-body systems.
Our findings offer valuable insights into the role of global inconsistencies in QFTs, which underscores studying QFTs in the space of coupling constants instead of focusing on just a specific coupling. They demonstrate that it is possible to constrain the low-energy dynamics of strongly coupled QFTs like massless quantum chromodynamics by analyzing their anomalies.
Owing to these significant contributions to the field of quantum physics, this study was honored with The Outstanding Paper Award from the Physical Society of Japan.

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