Gravitational chiral anomaly and anomalous transport for fields with spin 3/2

Abstract

In a fluid with vorticity and acceleration, an axial current arises in the third order of gradient expansion, the corresponding phenomenon can be called the Kinematical vortical effect (KVE). It has recently been shown that the KVE while existing in the absence of gravitational fields, is nonetheless associated with effects in curved space-time, namely with the gravitational chiral quantum anomaly. In this paper, we find the KVE transport coefficients using the Zubarev quantum-statistical density operator for the Rarita-Schwinger-Adler theory, which includes massless fields with spins 3/2 and 1/2, and demonstrate the relationship with the gravitational anomaly. A prediction is made about the possible form of the transport coefficients for massless fields with arbitrary spin.