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Reflection positivity and invertible topological phases

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arxiv 1604.06527 v6 pith:6UDVYWA4 submitted 2016-04-22 hep-th cond-mat.str-elmath-phmath.ATmath.MP

Reflection positivity and invertible topological phases

classification hep-th cond-mat.str-elmath-phmath.ATmath.MP
keywords fieldtheorytopologicalgroupsymmetryhomotopyinvertiblephases
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 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.

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Cited by 16 Pith papers

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