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Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
by Salvatore D. Pace, Ömer M. Aksoy, Ho Tat Lam
Submission summary
| Authors (as registered SciPost users): | Ömer Mert Aksoy · Salvatore D. Pace |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00075v2 (pdf) |
| Date accepted: | Nov. 24, 2025 |
| Date submitted: | Oct. 30, 2025, 4:31 p.m. |
| Submitted by: | Salvatore D. Pace |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We extend the Symmetry Topological Field Theory (SymTFT) framework beyond internal symmetries by including geometric data that encode spacetime symmetries. Concretely, we enrich the SymTFT of an internal symmetry by spacetime symmetries and study the resulting symmetry-enriched topological (SET) order, which captures the interplay between the spacetime and internal symmetries. We illustrate the framework by focusing on symmetries in ${1+1}$D. To this end, we first analyze how gapped boundaries of ${2+1}$D SETs affect the enriching symmetry, and apply this within the SymTFT framework to gauging and detecting anomalies of the ${1+1}$D symmetry, as well as to classifying ${1+1}$D symmetry-enriched phases. We then consider quantum spin chains and explicitly construct the SymTFTs for three prototypical spacetime symmetries: lattice translations, spatial reflections, and time reversal. For lattice translations, the interplay with internal symmetries is encoded in the SymTFT by translations permuting anyons, which causes the continuum description of the SymTFT to be a foliated field theory. Using this, we elucidate the relation between Lieb-Schultz-Mattis (LSM) anomalies and modulated symmetries and classify modulated symmetry-protected topological (SPT) phases. For reflection and time-reversal symmetries, the interplay can additionally be encoded by symmetry fractionalization data in the SymTFT, and we identify mixed anomalies and study gauging for such examples.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
Added a new paragraph at the end of the summary section---Section 1.1---summarizing the reflection enriched SymTFT example from Section 4 of the main text.
Added a remark after Eq 1.1 that in our paper, we only consider examples with $A_\mathcal{L}$ and $Q_\mathcal{L}$ abelian.
Removed the sentence ``Generalizations to non-invertible symmetries are conceptually straightforward.'' that appeared in the second paragraph of section 2.
Reworded the sentence ``each anyon in $\mathcal{A}$ carries no fractional $Q$ symmetry charge.'' to ``no anyons in $\mathcal{A}$ carry fractional $Q$ charge.''
Moved Figure 4 (which now appears as Figure 3) to the main text, and modified its caption to accommodate its new location.
Expanded footnote 22 to emphasize that we are assuming the modulated symmetries in Section 3.1 are anomaly-free.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)