- The paper demonstrates that merging 0-form and 1-form symmetries into a 2-group framework uncovers intricate ’t Hooft anomalies beyond traditional c-number phases.
- It employs symmetry defects and background 2-group gauge fields to systematically analyze both gapped and gapless systems in quantum field theory.
- Its findings challenge conventional symmetry implementations by revealing how 2-group structures influence symmetry fractionalization in topological phases.
On 2-Group Global Symmetries and Their Anomalies
The paper by Benini, Cordova, and Hsin offers a comprehensive exploration of the interplay between 2-group global symmetries and their corresponding anomalies within quantum field theories (QFTs). Central to this discourse is the notion that both 0-form and 1-form symmetries can integrate into a unified structure known as a 2-group, which significantly impacts the interpretation and implementation of symmetries and corresponding anomalies in theoretical physics.
In traditional QFT, 0-form symmetries typically act on local operators, while 1-form symmetries have their influence on line operators. While higher-form symmetries are generally Abelian, the incorporation within a 2-group allows for a more intricate relationship resembling a categorical structure, where both components are interconnected through a concept known as a Postnikov class. The paper details explicit methodologies to identify these 2-group symmetries in QFTs, with specific examples across both gapped and gapless systems, enhancing the comprehension of non-Abelian interactions and implications in both discrete and continuous settings.
This paper shines a light on the underpinnings of global symmetries by employing symmetry defects, elucidating their topological nature, and demonstrating how the interplay of 2-group settings influences these. Specifically, symmetry defects manifest as higher-codimension operators with invariant correlation functions that epitomize the implementation of symmetries within topological sectors of QFTs.
In terms of anomalies, the paper elucidates the inherent characteristics and constraints by exploring 't Hooft anomalies within the field of 2-group symmetries. 't Hooft anomalies, in this context, emerge as obstructions that paint a richer picture than traditional c-number phases, demanding consideration of operator-valued anomalies, which reflect the inherent complexities associated with non-trivial 2-group global symmetries.
The authors extend the discourse to the theoretical implications of coupling quantum field theories to background fields. Specifically, when a QFT features a 2-group global symmetry, its appropriate interaction involves coupling to a 2-group gauge theory—a framework which supports both 1-form and 2-form background fields, adhering to the higher categorical nature of 2-group symmetries. These couplings are significant in deciphering how 2-groupward identities are impacted by anomalies observed within standard gauge transformations.
To explore the implications of their findings, Benini et al. present an array of examples, particularly emphasizing the dynamics of 3-dimensional TQFTs and the ensuing impact of global symmetries. Here, they stress that what has often been labeled as "obstruction to symmetry fractionalization" is, indeed, an embodiment of 2-group global symmetry. Their application to TQFTs extends into broad characterizations found in modular tensor categories, spotlighting the intrinsic 2-group symmetry that is integral to these field theories.
In summation, this paper elucidates the ramifications of embedding symmetry into more generalized structures than previously considered, challenging and expanding current theoretical methodologies, and providing fertile ground for future explorations and extensions of discrete and continuous symmetries in emergent quantum fields. The insights posited hold potential to refine understanding of dynamics at varied energy scales, offering a nuanced perspective of global symmetries’ roles both in isolation and interaction within theoretical models.