Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid

Abstract

In (1+1) dimensional hydrodynamics in presence of the gravitational anomalies, the constitutive relations for the stress tensor contain the response parameters ${\bar{C}}_1$, ${\bar{C}}_2$ and the gravitation anomaly coefficients $c_g$, $c_w$. Here it is shown that they are related by the two relations ${\bar{C}}_1=4{\pi }^2{c}_w$ and ${\bar{C}}_2=8{\pi }^2{c}_g$. This agrees with the earlier findings. I argue that the Israel-Hartle-Hawking vacuum is the natural boundary condition which leads to such relation. Finally, the possible physical implications are discussed.

Revised version, to appear in JHEP

References in corpus (4)

• Gravitational Anomaly and Transport
• Noether current from the surface term of gravitational action, Virasoro algebra and horizon entropy
• Hawking Radiation, Covariant Boundary Conditions and Vacuum States
• Hydrodynamics in 1+1 dimensions with gravitational anomalies

Cited by in corpus (7)

• Anomalies and Entanglement Entropy
• Magnetoconductivity in chiral Lifshitz hydrodynamics
• Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters
• Constitutive relations and response parameters in two dimensional hydrodynamics with gauge and gravitational anomalies
• Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions
• Gravitational anomalies and one dimensional behaviour of black holes
• Thermal scalar field stress tensor on a two dimensional black hole and its near horizon properties