Analog of the Gravitational Anomaly in Topological Chiral Superconductors

G. E. Volovik*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


It is known that the contribution of torsion to the equation for the chiral Weyl fermions can be equivalently considered in terms of the axial U(1) gauge field. In this scenario the gravitational field transforms to the U(1) gauge field. Here we show that in chiral superconductors the opposite scenario takes place: the electromagnetic U(1) field serves as the spin connection for the Bogoliubov fermionic quasiparticles. As a result the electromagnetic field gives rise to the gravitational anomaly, which contains the extra factor 1/3 in the corresponding Adler–Bell–Jackiw equation as compared with the conventional chiral anomaly. We also consider the gravitational anomaly produced in neutral Weyl superfluids by the analog of the gravitational instanton, the process of creation and annihilation of the 3D topological objects – hopfions. The gravitational instanton leads to creation of the chiral charge.

Original languageEnglish
Pages (from-to)538-541
Number of pages4
JournalJETP Letters
Issue number8
Early online date2021
Publication statusPublished - Apr 2021
MoE publication typeA1 Journal article-refereed


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