2000 character limit reached
Gravitational Chern-Simons form and Chiral Gravitational Anomaly in Fluid Mechanics (2405.09751v2)
Published 16 May 2024 in hep-th and cond-mat.str-el
Abstract: We show that the hydrodynamic of the perfect fluid admits a deformation that includes a chiral gravitational (or mixed) anomaly alongside the chiral current anomaly. The deformation introduces the gravitational Chern-Simons term and an analog of an axion in fluid mechanics, and features fluid spin-current and anomaly induced spin-orbit interaction.
- The particle density of the reservoir n¯¯𝑛\overline{n}over¯ start_ARG italic_n end_ARG, and the density ratio n¯/n¯𝑛𝑛\bar{n}/nover¯ start_ARG italic_n end_ARG / italic_n are analogous with entropy and a specific ‘entropy’ of baroclinic flows. A view on entropy as a massless fluid constituent is discussed in Carter .
- In the Abelian case the Chern number takes an even value on singular configurations: vortices and magnetic lines. The value of the Pontryagin number for spin 4-surfaces is an even integer in multiples of 24.
- In homentropic and barotropic flows considered in abanov2022axial ; wiegmann2022chiral ; AW2 ; wiegmann2023Hamilton ; Abanov_Cappelli the enthalpy is not an independent quantity. It is a given function of the momentum pμsubscript𝑝𝜇p_{\mu}italic_p start_POSTSUBSCRIPT italic_μ end_POSTSUBSCRIPT. Consequently, the vorticity form is degenerate and Ω∧Ω=0ΩΩ0\Omega\wedge\Omega=0roman_Ω ∧ roman_Ω = 0. We do not consider this case here.
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