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Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions
by Da-Chuan Lu
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Submission summary
| Authors (as registered SciPost users): | Da-Chuan Lu |
| Submission information | |
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| Preprint Link: | scipost_202304_00022v1 (pdf) |
| Date accepted: | 2023-05-10 |
| Date submitted: | 2023-04-27 01:22 |
| Submitted by: | Lu, Da-Chuan |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space $G/K$, where $G$ is the UV symmetry and $K$ is generated by ${\mathfrak k}={\mathfrak h}_1\cap {\mathfrak h}_2$, and ${\mathfrak h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. With this specific target space, the symmetry defects in both SSB phases are on equal footing, and their intertwinement is captured by the WZW term. The DQCP transition is then tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with the WZW term to the background gauge field, the 't Hooft anomaly of this theory can be determined. The bulk symmetry-protected topological (SPT) phase that cancels the anomaly is described by the relative Chern-Simons term in odd spacetime dimensions or mixed $\theta$ term in even dimensions. We construct and discuss a series of models with Grassmannian symmetry defects in 3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with the WZW term.
Author comments upon resubmission
In our current manuscript, we use embedding to resolve the homotopy group with discrete generators, such that the homotopy group of the larger space contains integer-valued defects, which can be written in differential forms. This embedding is not directly related to the issues in the aforementioned reference, but it is still worth mentioning. For (1), since G/K contains all the information of topological defects in both symmetry-breaking phases, it is a suitable larger space to consider and reproduce the correct topological charges. For (2), we didn't consider the high codimensional topological defects, so it is unrelated to the 5th-degree bordism group. But for the anomaly matching using the Wess-Zumino-Witten term, this Z2 torsion part is relevant to the sign of the WZW term, and could be determined from the UV theory (please see arXiv:2009.00033, arXiv:2009.04692).
List of changes
1- Add clarification for bulk SPT in even spacetime dimension, the bulk theory would be mixed $\theta$ term. The gauged WZW term can be written in terms of a one-lower-degree form then.
2- Add references related to the bordism calculation of the anomalies.
3- Add more future directions which are relevant to this formalism.
Published as SciPost Phys. Core 6, 047 (2023)