Reflection positivity and invertible topological phases
By D. Freed, M. Hopkins. Geometry and Topology, 2016
400 citations recorded by the source corpus.
We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/73d2288eb66cb6ecf797578233bf04a6a1082402
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
In Nuclear and High Energy Physics
Citations in the corpus
- Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “The underlying topological cohomology class is the deformation class of the invertible field theory, as studied in [50].”
- Average Symmetry-Protected Topological Phases (2022, background): “The classification of clean 3D TIs in class AII is Z32[46, 72, 73].”
- Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, background): “Formally, one may interpret this ❩8 classification from the extended version of group super-cohomology [81–83] or the cobordism group [84, 85].”
- On 2-group global symmetries and their anomalies (2018, methodology): “In particular, to characterize the anomalies that we study we do not require the more sophisticated cobordism theory discussed in [26–28,12].”