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2021 Reflection positivity and invertible topological phases
Daniel S Freed, Michael J Hopkins
Geom. Topol. 25(3): 1165-1330 (2021). DOI: 10.2140/gt.2021.25.1165

Abstract

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 10–fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.

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Daniel S Freed. Michael J Hopkins. "Reflection positivity and invertible topological phases." Geom. Topol. 25 (3) 1165 - 1330, 2021. https://doi.org/10.2140/gt.2021.25.1165

Information

Received: 12 July 2016; Revised: 3 October 2019; Accepted: 29 October 2019; Published: 2021
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/gt.2021.25.1165

Subjects:
Primary: 55N22, 57R90, 81T45, 81T50, 82B99

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 3 • 2021
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