Differential $KO$-theory via gradations and mass terms

Gomi, Kiyonori; Yamashita, Mayuko

doi:10.48550/arxiv.2111.01377

Cited by 5 publications

(13 citation statements)

References 24 publications

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“…However, here we would like to pretend that Eq. (2.57) can be extended to more general fermion cases, perhaps by utilizing the result of [GY21]. In addition, the result here is already reported in the references mentioned above.…”

Section: Effective Action From Symmetry Breaking Masssupporting

confidence: 66%

“…The definition of a superconnection will be reviewed in Section 3.1. For the math literature regarding the superconnection and the relevant index theorem, see [Qui85,Kah11,GY21]. In particular, this approch enables us to write down an explicit formula for the Berry curvature B:…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…The purpose of this paper is to provide new methods to calculate the Berry phases and the Berry curvatures for more general theories of massive Dirac fermions. This will be done by first relating the Berry phase of a d-dimensional fermion system to a certain (d + 1)-dimensional η-invariant, and then invoking the Atiyah-Patodi-Singer (APS) index theorem for superconnections [Qui85,Kah11,KS21,GY21]. In particular, we provide an explicit formula computing the Berry curvature for such theories.…”

mentioning

confidence: 99%

“…In particular, we provide an explicit formula computing the Berry curvature for such theories. The index theorem necessary for the generalization to Majorana fermions is studied in [GY21].…”

mentioning

confidence: 99%

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Higher Berry Phase of Fermions and Index Theorem

Choi,

Ohmori

2022

Preprint

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When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background fields in the long-distance limit. The set of background fields can include spacetimedependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory. We study such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters using the Atiyah-Patodi-Singer index theorem for superconnections. In particular, the response to an infinitesimal modulation of the mass is encoded into a higher analog of the Berry curvature, for which we provide a general formula. When the Berry curvature vanishes, the invertible theory can still be nontrivial if there is a remaining torsional Berry phase, for which we list some computable examples.

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Section: Effective Action From Symmetry Breaking Masssupporting

confidence: 66%

Section: Summary Of Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Higher Berry Phase of Fermions and Index Theorem

Choi,

Ohmori

2022

Preprint

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“…We do not necessarily restrict our attention to massless fermions to take into account the possibility of coupling space anomalies of the type discussed in[51][52][53][54]. When we vary parameters in P of the theory T , some massive modes may become massless at some points of P and they can produce anomalies.…”

mentioning

confidence: 99%

Heterotic global anomalies and torsion Witten index

Yonekura¹

2022

Preprint

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We study the structure of anomalies in general heterotic string theories by considering general 2-dimensional N = (0, 1) supersymmetric quantum field theories (SQFTs), without assuming conformal invariance nor the correct central charges. First we generalize the precise notion of the B-field introduced by Witten. Then we express the target space anomalies by invariants of SQFTs. Perturbative anomalies correspond to the Witten index of some class of SQFTs, while global anomalies correspond to a torsion version of the Witten index. The torsion index gives some of the invariants of SQFTs suggested by topological modular forms, and is expected to be zero for the cases that are relevant to actual heterotic string theories.

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Higher Berry phase of fermions and index theorem

Choi

Ohmori

2022

J. High Energ. Phys.

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When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background fields in the long-distance limit. The set of background fields can include spacetime-dependent coupling constants, in which case we call the corresponding invertible theory a parameterized invertible field theory. We study such parameterized invertible field theories arising from free Dirac fermions with spacetime-dependent mass parameters using the Atiyah-Patodi-Singer index theorem for superconnections. In particular, the response to an infinitesimal modulation of the mass is encoded into a higher analog of the Berry curvature, for which we provide a general formula. When the Berry curvature vanishes, the invertible theory can still be nontrivial if there is a remaining torsional Berry phase, for which we list some computable examples.

show abstract

Differential $KO$-theory via gradations and mass terms

Cited by 5 publications

References 24 publications

Higher Berry Phase of Fermions and Index Theorem

Higher Berry Phase of Fermions and Index Theorem

Heterotic global anomalies and torsion Witten index

Higher Berry phase of fermions and index theorem

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