Anomaly inflow and thermal equilibrium

TL;DR

This work develops a general, local description of anomaly-induced transport in hydrostatic states by constructing a local anomalous generating functional $W_{anom}$ from the anomaly polynomial ${\bm{\mathcal{P}}}$ and Chern–Simons forms, with hatted connections enabling a manifestly covariant treatment. By identifying the abelian U(1) isometry with Euclidean time, the authors relate $W_{anom}$ to the thermodynamic partition function and extract covariant anomaly-induced currents via the vector $\mathbf{V}_{\bm{\mathcal{P}}}$, as well as Bardeen–Zumino polynomials and transgression relations. The formalism is extended from abelian to non-abelian, gravitational, and mixed anomalies, and a covariant hydrostatic framework is developed, including a covariant formulation of hydrostatics, electric-magnetic decompositions, and the role of hatted connections. The results connect anomaly inflow, transgression, and hydrodynamics, yielding explicit expressions for anomaly-driven transport in equilibrium and clarifying how rational and transcendental anomaly terms arise and relate to hydrodynamic constraints. The approach provides a powerful tool for computing hydrostatic correlators in the presence of anomalies and sets the stage for quantifying transcendental contributions in follow-up work.

Abstract

Using the anomaly inflow mechanism, we compute the flavor/Lorentz non-invariant contribution to the partition function in a background with a U(1) isometry. This contribution is a local functional of the background fields. By identifying the U(1) isometry with Euclidean time we obtain a contribution of the anomaly to the thermodynamic partition function from which hydrostatic correlators can be efficiently computed. Our result is in line with, and an extension of, previous studies on the role of anomalies in a hydrodynamic setting. Along the way we find simplified expressions for Bardeen-Zumino polynomials and various transgression formulae

Figures (1)

• Figure 1: Schematic diagram of the inflow mechanism where the manifold $\mathcal{M}$ is depicted as a semi-infinite cylinder and $\partial \mathcal{M}$ as its boundary. The current $J_{Hall}^M$ defined on the manifold $\mathcal{M}$ is conserved but transfers charge to the boundary theory on $\partial\mathcal{M}$ rendering it anomalous. The anomalous boundary current gets a contribution from the Bardeen-Zumino term $J_{BZ}^{\mu}$ associated with the flow of bulk charge and a consistent current associated with the theory defined on $\partial \mathcal{M}$.