Anomalous Chiral Superfluidity

TL;DR

The paper addresses how global flavor anomalies are manifested in a left-handed theory describing a chiral superfluid, using a gauged Wess-Zumino-Witten action to capture anomaly effects on flavored phonons. Employing a mean-field (tadpole) approximation, it shows that the gauge-invariant, symmetric part of the energy-momentum tensor renormalizes to an ideal-fluid form, while the normal current acquires anomalous corrections that reflect the underlying flavor anomalies; the anomalous current structure is tied to the WZW term, with the anomaly equation expressed as $dJ_L^a = -\frac{C}{8} d^{abc} F_L^b F_L^c$. Hydrodynamic interpretation identifies the phonon field expectation value with the local superfluid velocity, yielding relations such as $\langle \Pi_r^a\rangle \approx \mu^a v$ and $F_r^2 = (\epsilon+p)/((N-1)\mu^2)$, alongside Debye-counted phonon contributions. The Adler-Bardeen non-renormalization theorem is discussed as implying that quantum vertex corrections would cancel the mean-field anomalous contributions, stressing the distinction between mean-field results and full quantum corrections; the work highlights potential relevance to dense QCD phases, holographic QCD at finite density, and related long-wavelength, time-odd superfluid phenomena.

Abstract

We discuss both the anomalous Cartan currents and the energy-momentum tensor in a left chiral theory with flavour anomalies as an effective theory for flavored chiral phonons in a chiral superfluid with the gauged Wess-Zumino-Witten term. In the mean-field (leading tadpole) approximation the anomalous Cartan currents and the energy momentum tensor take the form of constitutive currents in the chiral superfluid state. The pertinence of higher order corrections and the Adler-Bardeen theorem is briefly noted.