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(Non)-Renormalization of the Chiral Vortical Effect Coefficient

Siavash Golkar, Dam T. Son

TL;DR

This work analyzes whether the temperature dependent part of the chiral vortical effect (CVE) coefficient is renormalized by interactions. Using a Coleman-Hill style diagrammatic argument, it proves non-renormalization for Yukawa-coupled fermions at zero chemical potential and links the CVE to a dimensionally reduced 3D Chern-Simons term, yielding a canonical value tied to $\sum_{n=1}^\infty n = -1/12$. However, when dynamical gauge fields are present, radiative corrections arise even at large $N$, with a leading two-loop contribution $\sigma^\mathcal{V}_{\text{Correction}} = \frac{g^2 C(r) d(G)}{48 \pi^2} T^2$. The work also shows that the 3D CS level is quantized under appropriate global conditions, and discusses how global anomalies may constrain the actual CVE value beyond the perturbative picture. These results clarify when anomaly-induced transport is protected and highlight the role of global, not just local, anomaly structure in determining CVE observables.

Abstract

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula $\sum_{n=1}^\infty n=-1/12$. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large $N$ limit.

(Non)-Renormalization of the Chiral Vortical Effect Coefficient

TL;DR

This work analyzes whether the temperature dependent part of the chiral vortical effect (CVE) coefficient is renormalized by interactions. Using a Coleman-Hill style diagrammatic argument, it proves non-renormalization for Yukawa-coupled fermions at zero chemical potential and links the CVE to a dimensionally reduced 3D Chern-Simons term, yielding a canonical value tied to . However, when dynamical gauge fields are present, radiative corrections arise even at large , with a leading two-loop contribution . The work also shows that the 3D CS level is quantized under appropriate global conditions, and discusses how global anomalies may constrain the actual CVE value beyond the perturbative picture. These results clarify when anomaly-induced transport is protected and highlight the role of global, not just local, anomaly structure in determining CVE observables.

Abstract

We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula . We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large limit.

Paper Structure

This paper contains 8 sections, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Calculation of the CVE coefficient
  3. Coupling To Scalars
  4. Coupling To Gauge Fields
  5. Connection To 3 Dimensional Chern-Simons Term
  6. Quantization Of The Level
  7. Zero Coupling Example
  8. Conclusion

Figures (3)

  • Figure 1: (a) A generic diagram at finite coupling. The internal lines are the sccalar field and the external lines are the graviton and the axial $U(1)$ field. (b) An $n$ scalar effective vertex. We can get all diagrams of type (a) by contracting the external scalar lines on type (b) diagrams.
  • Figure 2: The two diagram classes.
  • Figure 3: (a) The only class of diagrams with non-vanishing corrections to the CVE in the large $N$ limit. (b) The leading order diagram. (c) After replacing the leading order diagram with the effective vertex $J^\mu_\text{Anom}$. The triangle vertex represents the anomalous effect of the triangle diagram.