Spacetime symmetry-enriched SymTFT: LSM anomalies, modulated symmetries and beyond

Abstract: Symmetry Topological Field Theory (SymTFT) is a framework that allows one to capture certain universal properties of gapped and gapless phases of matter with a symmetry from the perspective of topological field theory in one-higher dimension. This approach has been very fruitful in understanding gapped and gapless phases with internal generalized symmetries, their anomalies and dualities between them. In this talk, I will describe one approach to extend the SymTFT framework to incorporate spacetime symmetries. Concretely, I will show that a topological order that is enriched by spacetime symmetries can act as a SymTFT that encodes the interplay between the spacetime and internal symmetries. I will provide concrete examples focusing on symmetries in 1+1D: 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. I will show how this construction reveals 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, which I will use to identify mixed anomalies and study gauging for such examples.

condensed mattergeneral relativity and quantum cosmologyHEP - latticeHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

Quantum Theories of Fields, Matter, and Strings

Series comments: A series of talks covering a broad range of topics in theoretical physics, including high energy theory, condensed matter, and string theory.

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