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Anomaly Induced Transport in Arbitrary Dimensions

R. Loganayagam

TL;DR

This work formulates a general, off-shell framework for anomaly-induced transport in arbitrary even dimensions, ensuring compatibility with the second law at any order in the derivative expansion. It derives an explicit off-shell solution for the anomaly-related heat and charge currents and introduces a Gibbs-current-like object that encodes the transport, including first-law and Onsager-type relations. In 4d, the authors show that through a frame transformation to the Landau frame, their general solution reproduces Son-Surowka’s results, while highlighting the distinction between on-shell and off-shell analyses. The discussion points toward deeper connections to index theory and potential holographic/gravity dual interpretations, as well as finite-temperature corrections and gravitational anomalies. Overall, the paper provides a unified, high-dimensional perspective on how global anomalies govern non-dissipative transport in relativistic fluids.

Abstract

Motivated by the consistency of a global anomaly with the second law of thermodynamics, we propose a form for the anomaly induced charge/energy transport in arbitrary even dimensions. In a given dimension, this form exhausts all second law constraints on anomaly induced transport at any given order in hydrodynamic derivative expansion. This is achieved by solving the second law constraints off-shell without resorting to hydrodynamic equations at lower orders. We also study various possible finite temperature corrections to such anomaly induced transport coefficients.

Anomaly Induced Transport in Arbitrary Dimensions

TL;DR

This work formulates a general, off-shell framework for anomaly-induced transport in arbitrary even dimensions, ensuring compatibility with the second law at any order in the derivative expansion. It derives an explicit off-shell solution for the anomaly-related heat and charge currents and introduces a Gibbs-current-like object that encodes the transport, including first-law and Onsager-type relations. In 4d, the authors show that through a frame transformation to the Landau frame, their general solution reproduces Son-Surowka’s results, while highlighting the distinction between on-shell and off-shell analyses. The discussion points toward deeper connections to index theory and potential holographic/gravity dual interpretations, as well as finite-temperature corrections and gravitational anomalies. Overall, the paper provides a unified, high-dimensional perspective on how global anomalies govern non-dissipative transport in relativistic fluids.

Abstract

Motivated by the consistency of a global anomaly with the second law of thermodynamics, we propose a form for the anomaly induced charge/energy transport in arbitrary even dimensions. In a given dimension, this form exhausts all second law constraints on anomaly induced transport at any given order in hydrodynamic derivative expansion. This is achieved by solving the second law constraints off-shell without resorting to hydrodynamic equations at lower orders. We also study various possible finite temperature corrections to such anomaly induced transport coefficients.

Paper Structure

This paper contains 8 sections, 1 theorem, 56 equations, 1 table.

Table of Contents

  1. Introduction
  2. Basic formalism
  3. Anomalous transport in General dimensions
  4. Comparison with Son-Surowka result
  5. Discussion
  6. Finite temperature corrections to anomaly-induced transport
  7. Explicit expressions in various cases
  8. Notation

Key Result

Theorem 1

Consider a $\mathcal{V}_{anom}$ of the form where $\mathfrak{f}$ and $\mathfrak{g}$ are some Taylor-expandable functionsat the origin (i.e., are analytic at the origin). Construct from this the following currents Then they satisfy If we only want the parts relevant to $2n$ spacetime dimensions, we can take treat $\mathfrak{f}$ and $\mathfrak{g}$ as $(n+1)$th and $(n-1)$th degree homogeneous pol

Theorems & Definitions (1)

  • Theorem