Abstract
The anomalous currents of two-flavor chiral nuclear matter in the presence of chiral imbalance are computed, using recently developed methods exploiting generalized transgression, which facilitates the evaluation of both the equilibrium partition function and the covariant currents. The constitutive relations for both the broken and unbroken phase of the theory are studied and the out-of-equilibrium nondissipative transport coefficients determined. In the superfluid phase, the vector covariant currents exhibit nondissipative chiral electric, magnetic, and vortical effects, the latter governed by chiral imbalance.
Highlights
The physical sources, can be obtained from its nonlocal piece
The vector covariant currents exhibit nondissipative chiral electric, magnetic, and vortical effects, the latter governed by chiral imbalance
In a previous paper [32], we used differential geometry to obtain explicit operative expressions allowing the computation of the equilibrium partition function of fluids in the presence of quantum (’t Hooft) anomalies, as well as the construction of the various currents associated with the corresponding global symmetries
Summary
For the reader’s convenience and to make our presentation self-contained, we briefly summarize the formalism and main results of ref. [32]. The appropriate Chern-Simons form preserving the invariance under vector gauge transformations takes the form (see [32] for details) ω50(A, FV , FA) = 6Tr. After implementing dimensional reduction and writing everything in terms of the corresponding KK-invariant fields (V0, Vi) and (A0, Ai) [cf (2.14)], we find that the invariant and anomalous parts of the anomalous functional can be computed by the likes of eqs. As for the anomaly-induced component of the energy-momentum tensor, its dual twoform can be obtained by taking functional derivatives of the invariant part of the effective action [32]. The differential geometry approach to the computation of covariant currents is specially useful when applied to systems with spontaneous symmetry breaking In this case, the dynamics of NG bosons is largely determined by the anomaly through the following prescription for the WZW effective action [1].
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