Analog of gravitational anomaly in topological chiral superconductors

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.

arXiv comment4 pages, no figures, JETP Letters 113, issue 8 (2021)

References in corpus (7)

• Knots and Particles
• Momentum creation by vortices in 3He experiments as a model of primordial baryogenesis
• Torsion, Parity-odd Response and Anomalies in Topological States
• On the chiral anomaly in non-Riemannian spacetimes
• Emergent Horava gravity in graphene
• Nieh-Yan Anomaly: Torsional Landau Levels, central charge and anomalous thermal Hall effect
• Effective action and electromagnetic response of topological superconductors and Majorana-mass Weyl fermions

Cited by in corpus (4)

• Axial-Current Anomaly in Euler Fluid
• Chiral Vortical Effect in Extended Rarita-Schwinger Field Theory and Chiral Anomaly
• Gravitational chiral anomaly for spin 3/2 field interacting with spin 1/2 field
• The Sugawara-Sommerfield construction including canonical spin current