Pin TQFT and Grassmann integral

Kobayashi, Ryohei

doi:10.1007/jhep12(2019)014

Cited by 27 publications

(22 citation statements)

References 40 publications

(106 reference statements)

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“…5 In the case of antiunitary symmetries it requires, for example, learning how to define spin TQFTs on unoriented manifolds, which is an open problem. Numerous interesting partial results have been obtained, however [18,[36][37][38][39][40][41][42][43]. 6 One could also study the reduction of the anomaly class on more general manifolds, potentially detecting more anomalies.…”

Section: Jhep11(2021)142mentioning

confidence: 99%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

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Section: Jhep11(2021)142mentioning

confidence: 99%

Global anomalies on the Hilbert space

Delmastro

Gaiotto

Gomis

2021

J. High Energ. Phys.

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“…For recent work on this invertible phase, see e.g. [47][48][49]. The ABK invariant can be thought of as the effective action of the Kitaev chain protected by time-reversal.…”

Section: Invertible Phase For Pin − Structurementioning

confidence: 99%

Topological superconductors on superstring worldsheets

et al. 2020

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We point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible phases, or equivalently topological superconductors, on the worldsheet. This allows us to find that the unoriented Type 00 string theory with \Omega^2=(-1)^{f}Ω2=(−1)f admits different GSO projections parameterized by nn mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of nn boundary Majorana fermions then leads to the classification of D-branes by KO^n(X)\oplus KO^{-n}(X)KOn(X)⊕KO−n(X) in these theories, which we also confirm by the study of the D-brane boundary states. Finally, we show that there is no essentially new GSO projection for the Type II worldsheet theory by studying the relevant bordism group, which classifies corresponding invertible phases. In two appendixes the relevant bordism group is computed in two ways.

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“…In particular, these anomalies do not have any obvious imprint on the correlation functions of local operators and so the above logic does not apply. There are general constructions [13][14][15][16][17] showing that large classes of anomalies for discrete symmetry groups can be matched by a suitable symmetry preserving topological field theory.…”

Section: Introductionmentioning

confidence: 99%

Anomaly constraints on gapped phases with discrete chiral symmetry

Córdova

Ohmori

2020

Phys. Rev. D

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We prove that in ð3 þ 1Þd quantum field theories with Z N symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are frequently present in gauge theories as we illustrate in examples. Our results also constrain the long-distance behavior of certain condensed matter systems such as Weyl-semimetals and may have applications to crystallographic phases with symmetry protected topological order. These results may be viewed as analogs of the Lieb-Schultz-Mattis theorem for continuum field theories.

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Pin TQFT and Grassmann integral

Cited by 27 publications

References 40 publications

Global anomalies on the Hilbert space

Global anomalies on the Hilbert space

Topological superconductors on superstring worldsheets

Anomaly constraints on gapped phases with discrete chiral symmetry

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