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.
Highlights
INTRODUCTIONThe Rarita-Schwinger spin 3=2 theory is an essential element of supergravity theories [1] and grand unification models [2], in which it is used for anomaly cancellation
The coefficients 5 in the terms T2 and μ2 were obtained as a result of summation 6 − 1 1⁄4 5, where 6 is the contribution of the interaction terms, and −1 is the contribution of the pure Rarita-Schwinger field. This distinguishes the above calculation from the calculation of the chiral anomaly and chiral separation effect (CSE) in [7,16], where the additional field did not contribute
We have shown an exact correspondence between hydrodynamics and quantum field theory: the coefficient in front of the chiral anomaly (2.5) corresponds to the coefficient in chiral vortical effect (CVE) (3.13)
Summary
The Rarita-Schwinger spin 3=2 theory is an essential element of supergravity theories [1] and grand unification models [2], in which it is used for anomaly cancellation. The Rarita-Schwinger theory of fields is characterized by a number of pathologies [5–8], in particular, the singular Dirac bracket turns out to be in the weak-field limit and there is the discontinuity in the number of degrees of freedom when an external field is present. These problems were overcome in [7] by introducing a field with spin 1=2, which made it possible to construct a consistent quantum field perturbation theory and calculate the chiral quantum anomaly.
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