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Reflection positivity and
invertible topological phases
Daniel S Freed and Michael J Hopkins |
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Geometry & Topology 25 (2021) 1165–1330
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Abstract |
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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 type. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic –fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem. |
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Keywords
topological phases, invertible field theory, reflection
positivity, symmetry protected topological phases, free
fermions, topological field theory
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Mathematical Subject Classification 2010
Primary: 55N22, 57R90, 81T45, 81T50, 82B99
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References |
Publication
Received: 12 July 2016
Revised: 3 October 2019
Accepted: 29 October 2019
Published: 20 May 2021
Proposed: Peter Teichner
Seconded: Ralph Cohen, Ulrike Tillmann
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Authors |
| Daniel S Freed | |
| Department of Mathematics University of Texas Austin, TX United States |
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| Michael J Hopkins | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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