Analog of gravitational anomaly in topological chiral superconductors

TL;DR

This paper explores how electromagnetic fields act as spin connections in chiral superconductors, leading to a gravitational anomaly with a unique factor, and examines related phenomena in Weyl superfluids involving topological objects.

Contribution

It demonstrates that in chiral superconductors, the electromagnetic U(1) field functions as the spin connection, inducing a gravitational anomaly with a distinctive 1/3 factor in the anomaly equation.

Findings

Electromagnetic U(1) field acts as spin connection in chiral superconductors.

Gravitational anomaly in these systems includes a 1/3 factor in the Adler-Bell-Jackiw equation.

Creation of chiral charge via gravitational instantons in Weyl superfluids.

Abstract

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.