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

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 $\bar{C}_1 = 4π^2 c_w$ and $\bar{C}_2 = 8π^2 c_g$. 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.

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