Abstract
We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid. We see that there are 27 parity odd transport coefficients, of which 12 are non-vanishing in equilibrium. We use the equilibrium partition function method to express 7 of these in terms of the anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The remaining 5 are constrained by 3 relations which also involve the anomaly. We derive Kubo formulae for 2 of the transport coefficients and show these agree with that derived from the equilibrium partition function.
Highlights
Coefficients which occur at the first order in the derivative expansion have been related to quantum anomalies of the microscopic theory [1,2,3,4,5,6,7,8].1 Our goal is to see if a similar phenomenon occurs at the second order in the derivative expansion of the constitutive relations
We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid
The stress tensor and the charge current evaluated on this time independent solution can be obtained from the partition function by varying it with respect to the background metric and the gauge field
Summary
The aim of this note is to constrain the parity odd second order transport coefficients of an anomalous charged fluid in the presence of background electric and magnetic fields. Let us consider the expansion of the charge current Jμ and the stress tensor T μν in terms of the number of space time derivatives. From the table it can be seen that at second order in derivatives there are 27 parity odd transport coefficients which appear in the current and the stress tensor. Our goal is to constrain the transport coefficients Φi, χi and ∆i , using the existence of an equilibrium partition function It can be shown among these 27 terms only 12 can be non-zero in a time independent equilibrium fluid configuration. The rest ∆1, χ1, · · · χ4 are constrained by 3 relations which involve the anomaly and the bulk viscosity ζ
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