Constitutive relations and response parameters in two-dimensional hydrodynamics with gauge and gravitational anomalies

Abstract

We obtain the constitutive relations for the stress tensor and gauge current in (1 + 1) dimensional hydrodynamics in the presence of both gauge and gravitational (conformal as well as diffeomorphism) anomalies. The relations between response parameters and anomaly coefficients are also found. The role of the Israel Hartle Hawking vacuum is emphasised. Finally, in the absence of gauge fields, earlier results obtained by a hydrodynamic expansion are reproduced. *

Adiabatic hydrodynamics: the eightfold way to dissipation

“…This consistency of the equilibrium partition function gives a number of hydrostatic relations that we call as H F (for hydrostatic forbidden). 31 We will have more to say about these various categories in the course of our discussion.…”

“…Indeed any deviation from equilibrium can be measured by the temporal changes -we will make extensive use of the fact that δ B g µν and δ B A µ will capture the linear time dependence away from equilibrium in what follows. 31 Empirically, terms in Class HF appear to account for about a third of the total number of transport coefficients at a given order in the gradient expansion (beyond leading order). See tables 7 and 8 for a summary of the counting in a variety of examples.…”

Magnetoconductivity in chiral Lifshitz hydrodynamics

“…The various implications of quantum anomalies [1]- [3] on relativistic hydrodynamic systems [4] has been an active area of research for the past couple of decades 1 [5]- [7]. The fact that is well understood by now is that the presence of anomalies always induce transport processes in a relativistic hydrodynamic system without any effects of dissipation and thereby they do not contribute to the local entropy production with in the system itself [8]- [25]. Keeping the spirit of this intriguing fact, it is noteworthy to mention that the physics of (chiral) anomalies has attained renewed attention for the past one decade in the context of relativistic heavy ion collisions where during the early non equilibrium stages of the collision one might have an imbalance between the number of left handed and right handed quarks [26]- [28].…”

“…• Finally, we would like to mention about the last piece of information available above in (42) namely, 2α 3 ̺ ǫ+p which could be thought of as an effect arising due to the acceleration of the charged particles in the system. We identify this effect as the consequence of the acceleration term present in the constitutive relation of the charge current (25).…”

“…Note that in the Kubo formula of γ B one needs to take the zero momentum (k → 0) limit followed by a zero frequency (w → 0) limit which is quite reminiscent to that of the Kubo formula for anomalous transports [8]. This similarity stems from the fact that both of these transports are associated with the parity odd contributions to the constitutive relations (24) and (25). On the other hand, α 2 is the usual dissipative transport which is also reflected in its Kubo formula (62).…”