Chiral Vortical Effect in Extended Rarita-Schwinger Field Theory and Chiral Anomaly

TL;DR

This paper investigates the chiral vortical effect in a spin 3/2 Rarita-Schwinger field interacting with a spin 1/2 field at finite temperature and vorticity, revealing a new universal relation and its connection to chiral anomalies.

Contribution

It provides a detailed calculation of the CVE coefficient for spin 3/2 fields, highlighting the impact of interactions and proposing a potential universality and link to chiral anomalies.

Findings

CVE coefficient for spin 3/2 is 5, combining contributions from Rarita-Schwinger and spin 1/2 fields.

The coefficients for $$ and $T^2$ are proportional but not to the spin, indicating a new universality.

Results suggest a connection between gauge and gravitational chiral anomalies.

Abstract

We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $\mu^2$ and $T^2$ are proportional to each other, but not proportional to the spin, which indicates a possible new universality between the temperature-related and the chemical potential-related vortical effects. The results obtained allow us to speculate about the relationship between the gauge and gravitational chiral anomalies.