Abstract:

A new theory for spin 3/2 field, proposed by S. L. Adler, including the interaction between the Rarita-Schwinger field and the Dirac field, is considered. The density operator and Green’s functions are constructed for the case of finite temperature, chemical potential, and thermal vorticity. The vortical chiral current for spin 3/2 is found and the role of interaction with the spin 1/2 field is clearly demonstrated: the contribution of the interaction terms to the vortical conductivity is 6. Since the contribution from the Rarita-Schwinger field is -1, the total factor is 6-1=5 , which is in accordance with the Adler’s prediction for the gauge chiral anomaly for spin 3/2 and confirms the anomalous nature of the vortical current (equivalently: gives a derivation of the anomaly from hydrodynamics). At the next step, we found the gravitational chiral quantum anomaly for spin 3/2 and showed that it is -19 times larger than the anomaly for spin 1/2. The conformality of the theory is directly verified in the strong interaction limit at the level of one-loop three-point correlators. The results obtained allow us to discuss the relationship between the effects at a finite temperature in a vortical fluid and the Hawking radiation in space-time with the horizon. A review of the previous works will also be made.