Anomalous charged fluids in 1+1d from equilibrium partition function

TL;DR

This work analyzes parity-violating charged fluids in 1+1 dimensions by constructing a time-independent equilibrium partition function that encodes the anomaly. By enforcing CPT invariance and matching with hydrodynamic constitutive relations, the authors derive explicit coefficients for parity-odd corrections and show these constraints agree with those obtained from entropy considerations. The results reproduce the expected anomalous current and stress-tensor structure, and the derived entropy current aligns with previous analyses, reinforcing the partition-function approach as a robust tool for anomaly-induced hydrodynamics. The findings suggest a consistent framework across dimensions for relating equilibrium partition functions to non-dissipative hydrodynamic data.

Abstract

In this note we explore the constraints imposed by the existence of equilibrium partition on parity violating charged fluids in 1+1 dimensions at zero derivative order. We write the equilibrium partition function consistent with 1+1 dimensional CPT invariance and which reproduces the correct anomaly in the charge current. The constraints on constitutive relations obtained in this way matches precisely with those obtained using the second law of thermodynamics.