Spacetime symmetry-enriched SymTFT: From LSM anomalies to modulated symmetries and beyond, by Salvatore D. Pace, Ömer M. Aksoy, Ho Tat Lam

SciPost Physics Home Authoring Refereeing Submit a manuscript About Spacetime symmetry-enriched SymTFT: From LSM anomalies to modulated symmetries and beyond Salvatore D. Pace, Ömer M. Aksoy, Ho Tat Lam SciPost Phys. 20, 007 (2026) · published 14 January 2026 doi: 10.21468/SciPostPhys.20.1.007 pdf BiBTeX RIS Submissions/Reports 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.007TI - Spacetime symmetry-enriched SymTFT: From LSM anomalies to modulated symmetries and beyondPY - 2026/01/14UR - https://scipost.org/SciPostPhys.20.1.007JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 007A1 - Pace, Salvatore D.AU - Aksoy, Ömer M.AU - Lam, Ho TatAB - 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.ER - × @Article{10.21468/SciPostPhys.20.1.007, title={{Spacetime symmetry-enriched SymTFT: From LSM anomalies to modulated symmetries and beyond}}, author={Salvatore D. Pace and Ömer M. Aksoy and Ho Tat Lam}, journal={SciPost Phys.}, volume={20}, pages={007}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.007}, url={https://scipost.org/10.21468/SciPostPhys.20.1.007},} Ontology / Topics See full Ontology or Topics database. 't Hooft anomalies Discrete gauge theories Emergent phases Exactly solvable models Fractionalization Quantum spin chains Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Salvatore D. Pace, 1 Ömer M. Aksoy, 1 Ho Tat Lam 1 Massachusetts Institute of Technology [MIT] Funders for the research work leading to this publication David and Lucile Packard Foundation Heising-Simons Foundation National Science Foundation [NSF] Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung / Swiss National Science Foundation [SNF] Simons Foundation United States Department of Energy [DOE]