Dynamo seeds from gravitational torsional anomalies and de Sitter magnetized metrics

Abstract

Recently gravitational and Nieh–Yan (NY) chiral anomalies have been obtained in Riemann–Cartan space–time (L.C. Garcia de Andrade. Class Quantum Grav. 38(6), 065005 (2021). doi: 10.1088/1361-6382/abd25f ), where electrodynamics is encoded in the metric geometry. In this paper we follow the same pathway by obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized de Sitter metric (DSMM) without axial anomalies is proved. Unified theories à la Einstein, Eddington, and Schroedinger, called modified de Sitter metrics, present some novel features. First, we show that a pure DSMM in T4 does not induce gravitational anomalies. This is a motivation to study modifications of DSMM. NY torsional anomaly in DSMM teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-trivial anomalies are obtained from these metrics. Torsional anomaly, much used in condensed matter physics, does not vanish. From these deformed DSMM, we show that a dynamo equation with torsional gradient sources is valid from class III of the metrics but is torsionless sourced in class II. We show that in the gravitational anomaly of new deformed de Sitter metric one may cancel the gravitational anomaly, by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. A simple deformation leads to the existence of the NY density in the case of DSMM. This would be class IV of DSMM.